In a supranational entity with iirc nearly 500 million inhabitants, of course an individual doesn't have much of a say. What's worse, the EU has been rather undemocratic - there is a European Parliament, even if the elections for it tend to be a travesty in which people vote as if it were a national election, punishing or rewarding their government, but it has little power. The Lisbon Treaty improves this somewhat, but not by a lot - most power still lays in the hands of the Commission, which currently consists of one delegate of each country, selected by the government. Lisbon would reduce the size of the Commission to make it more efficient - currently the need to have one Commissary for each member state has meant that there are some whose responsibilities are rather limited at best and not exactly very efficient. This would however mean that smaller nations don't have a Commissary anymore, or at least not permanently (they'd rotate).

Something else that Lisbon will do is reduce the amount of things that require full unanimity among all the member states, in favour of a system where a proposal, in order to pass, needs to be supported by a certain percentage of the member states, whose population needs to reach a certain percentage of the total population.

The pros are that it should make the EU less unwieldy, that it'll modestly increase the powers of the European Parliament, and quite simply that it keeps the momentum going - rejecting Lisbon would put the EU in a funk and threaten the further operation. Of course, rejecting Lisbon would also make further expansion very difficult, and an inevitable side-effect of expansion is further diluting the power of each current member state.

To be honest, many people who have been against LT or its predecessor the European Constitution have been so for spurious reasons - voting to punish their national government because they disapproved of what it was doing, or because they have ridiculous paranoid theories about what it would mean (such as the inane misinformation campaign about the minimum wage mentioned in the article), and so on. Of course many people who voted *for* it also did so for the wrong reasons.
As for serious reasons, most people voting against it are really just voting against any further expansion of the EU, whether geographically or in terms of powers, or are protesting the current lack of democracy and transparence in the EU, even though Lisbon should offer some improvement in those things.

I don't think anyone in Ireland is against their country being in the EU, considering the EU has played a significant role in bringing it from backwards island to one of the richest countries in the world. And for small countries like Ireland, the current crisis has reminded people that having a shared currency and hence shared monetary policy, as well as to some extent economic policy, shields them from some bad things like devaluation or strongly fluctuating currency.

The UK of course doesn't have the euro, and is historically wary of the European continent and very attached to its independence and special position as island nation. For those reasons, it has always been less enthusiastic about Europe than its neighbours across the Channel, and the UK leads a group of European countries - the others vary, but the UK is invariably in that group - that think the EU should mostly limit itself to economics and some small other things, rather than the much more extensive role advocated by countries like Belgium, France and Germany. That division goes back all the way to the fifties, when the then-European Economic Community (of France, Germany, Italy, Belgium, the Netherlands and Luxembourg) had a rival in the European Free Trade Association (with the UK, Norway, Denmark, Sweden, Portugal, Switzerland and Austria). In 1973 the UK and Denmark joined the EEC along with Ireland, thus reducing the EFTA to a secondary role, and then later all the others except Norway and Switzerland joined as well.