The fact he owns ILM has nothing to do with Lucas's influence "as a director". If you said that Lucas was one of the key entrepreneurs that fundamentally changed the way blockbusters are made I'd agree more, but to call him the most influential director, implying his movies and work as a director are some of the most influential around is just plain unfair.

ILM's contribution to movie making is however hardly overlooked, though they're no longer as important and looked up to as they were back in 1990s and early 2000s (they lost quite a bit of their market share, in part thanks to being overpriced and for their sweat shop mentality that makes it more difficult for them to attract and keep the best people around as competitors have emerged all around, but also because computers have become much cheaper and it's now much easier to start a VFX company without having a financial empire (in Lucas's case, the profits of his SW toys and all), behind you.

You make it sound as if George Lucas had been behind the technical and creative innovations of ILM, or most of them. In fact, he's not been involved directly (and still isn't) very much at that level (even as a director he's more the type not to care that much how it's achieved as long as he gets the results he wants for the price he wants), and very often the innovations themselves have not even been ILM's own. And Lucas has people who really run ILM for him, of course. If ILM has been so omnipresent in the field, it's also a lot because their creation was a timely one and they've long been in a near monopoly position in Hollywood in the days when you couldn't learn those crafts anywhere but through apprenticeship with master craftsmen, and ILM had gathered most of the masters in one company (one of the innovations of ILM was to gather people from many different specialities who were working freelance, for studios or in their own small shops to one company who could offer many types of effects. That kind of company didn't really existed before ILM, and mind you, at first ILM wasn't offering the whole palette of specialities either. Most of the specialized people who worked on SW1 and ESB and even ROJ didn't work for ILM. Eventually, competitors arose, companies often founded by people who couldn't stand to work at ILM anymore.

When ILM was founded, Hollywood was already returning slowly to more SFX heavy movies (after the "depressive" seventies). Initially the company was created merely so Lucas could afford so many effect shots in one B-movie Fox had very little hopes and too little money for... the techniques used for ANH were not new, they were not invented by them. Blue screen, mattes, multi-passes optical compositing, matte paintings, models in stop-motion, puppets... all of that already existed, and some of those were almost as old as cinema itself, or more if they originated from stage theater. The people hired for ANH were some of the best around (a few were even the top players in their specialities, and already had a long cinematography under their belt), and they're the ones who started to innovate, essentially perfecting a bit some of the old techniques (it's in the order of finding ways to add more layers to a multi-pass shot before the image had degraded so much it couldn't be used. It was technical innovations - mostly at the engineering level, but hardly "groundbreaking".). So basically, when Lucas and his associates decided ILM would offer its services to clients, it's not cinematographic genius that was at work but business flair. Lucas has always had more than his share of that.

From 1982-83, ILM introduced many new work techniques (eg: people don't realize how groundbreaking technically the space battle at the end of ROTJ is - it pushed the old optical compositing technique to its physical limits), but Lucas' personal contribution is far more of the order of asking ILM to find ways to get him more ships in one shot. Few but people who work in VFX really understand how groundbreaking or not most of ILM's techniques have been over the years. They sure invested a lot in R&D at some point, and came up with impressive stuff (often seen in software companies's demo reels only, as they were not quite yet viable to use commercially for movies), but very often they're "innovations" are actually stuff that's been theorically feasible for years (eg: the impressive water effects in Perfect Storm), but that has sat on the shelf for years as processing power (for commercial use) simply didn't exist for such softwares to run, or to be used commercially.

The biggest and most groundbreaking achievement of Lucas's people (with some personal involvement, Lucas was himself an editor once, and very interested in the process) the one that most fundamentally changed cinema, is much lesser known and it was a revolutionary way to approach editing in a non-linear fashion with a system developped for ROTJ and dubbed the Edit Droid. The rights to that homemade system of Lucasfilms got sold to a third party, and after a decade or so of further development it became the Avid system, and that has sent a whole generation of editors to early retirement, and has changed postproduction workflow and possibilities pretty fundamentally (at first it sped up editing massively, after a few years as people were discovering its possibilities, it changed how directors and show creators even saw editing). There's a whole lot of things in theaters and even more on TV that would have been unthinkable before the introduction of computer-based non-linear editing.

The THX system and program was certainly groundbreaking too, though it improved on the existing Dolby system.

Then came digital effects and movies moved from using SFX to using VFX. ILM has been the prominent player, but again it owes a lot to the fact it enjoyed a near monopoly at the time and thus were the only ones who had the client list and profits to invest in buying the new toys as soon as they were emerging, and to be able to pay the people who could use them. But it's the new toys themselves which were the really groundbreaking stuff, not the fact they were used by talented people working for George Lucas. The real revolution in movie making was the switch to digital effects and it came from people like Montrealer Daniel Langlois, who invented Softimage (and who had directed a few years earlier the first full 3D animated short movie), the first 3D software suite that could viably be used for commercial movie making on a large scale (it's that revolutionary software suite that put 3D-animation in the hands of artists instead of programmers and mathematicians), and that itself relied on the fact Silicon Graphics had come up with powerful enough computers that didn't need anymore to be as big as two refrigerators (only as big as one, and half its height, the first time we bought a SGI) and that no longer cost millions. All the other early 3D developpers that survived (most didn't) the arrival of Softimage did so by building and improving on its innovations. Alias (another Canadian company, this time Ontarian) reinvented its own powerful but very unfriendly software that became Maya (still the leading software today). It's mainly those two companies that revolutionized VFX and made it possible for ILM's artists to make movies like Jurassic Park (the movie that catapulted Softimage to near monopole status it enjoyed for a few years), often with massive technical support from the engineers/developpers of Softimage or Alias (ILM often triggered innovations of their own by asking to be able to do this and that, getting Softimage and co.'s developpers to work to develop them, and when ILM had invested in the R&D they had exclusivity over those new modules or features for a while, thus the reason why they were the only ones who could do this or that). Another massively important landmark ILM gets wrongly credited by the general public was in fact due to the introduction of yet another Montréal-invented system, Discreet Logic's Flame, this time a very powerful tool for digital compositing and advanced image manipulation (motion tracking, notably). Many of the features of Flame were totally new (though they've become very common nowadays). Yeah, ILM were among the first to be able to afford one (and some of its artists had contributed as beta-testers), and it's how they could make Forest Gump's VFX. Most of the credit for innovation ought to go to the DL people who thought of developping a system that would be able to do new types of visual effects like this, though. ILM's achievements with them, and with 3D softwares, are more of an artistic nature, and they often shared that with director and writers who thought to have such stuff in their movies (and yeah, it includes Lucas who really pushed the enveloppe of what could be realistic to put in a movie with The Phantom Menace).

But as a director, Lucas isn't all that influential, and the movie for which he gets the most credit and accolades as filmmaker by cinema scholars today, the one studied in cinema schools, is THX-1138, not any of the SW.