One of the first things Ishamael said to LTT was "After this day, men will call you Kinslayer", as if he knew for certain that LTT was responsible for all the destruction in the palace. He couldn't have known for sure that was the case the moment he Traveled in there to confront LTT, a few paragraphs previously. Indicating, to me, that he spied on LTT before he actually confronted him at the beginning of the Prologue.

As for WHY he confronted LTT ... here's a Q&A from the 2004 wotmania interview with RJ:

Q: Did Ishamael come to Lews Therin Telamon’s palace in the prologue of Eye of The World to kill him?

RJ: No. To taunt him with his defeat. Ishamael would much rather have had Lews Therin alive and suffering from the knowledge of defeat, not to mention the murder of his wife and other blood kin, than simply dead.

That's basically what DSoM said above.

Having just watched LTT murder his family, I think Ishamael was feeling confident that LTT was so "out of it" that he could easily defend himself if LTT were to attack him. Ishy must have know the Taint had cause LTT to go crazy and do what he did, he just was surprised that the Taint had affected LTT so much that LTT didn't even recognize him.

I don't think he was really serious about converting LTT to the Shadow, although he did mention that if LTT were to convert, the Great Lord could bring Ilyena back for him. But, I think that was just typical Ishy dogma (to foreshadow how he'd treat Rand in the first 3 books) - I don't think he was really serious about it.

What he was really serious about was to see LTT suffering and humiliated, and to gloat. I don't think there was much more to it than that.