The ending theme from Lain (the song that plays during the credits and the "wire womb" picture) is named Toh-I Sakebi. Though not strictly Jpop, Lain's opening song is named Duvet and is performed by the group BoA. Two variations of Duvet can be found on the CD "Tall Snake": Lain/Cyberia Mix (a more techno version) and the acoustic version. If you've heard Duvet and liked it, I'd definitely suggest checking out "The Race of 1000 Camels" BoA's full CD, as it's quite good.
>soundtracks
There are actually three different soundtracks to Lain and one limited edition that few people know about. There's the SEL OST which has songs that play during the little cut scenes and such, Lain:Cyberia Mix, which are composed of songs from the series that have been altered and made to have more of a techno slant. There's also Lain:Bootleg, which is all the background music that *isn't* on the OST, the songs that play while Lain's having a conversation with Professor Hodgeson, while she's walking around her house, etc. I've also been told that the music on Bootleg is used in the PSX Lain game. Finally, the limited edition DVD has a song that isn't on either of the other CDs, "13th Floor Elevator." I can't place this song within the series, so I'm willing to bet it was meant to be included yet was cut at some point.
While I'm sure quite a few people know of it, the song that plays at the end of Evangelion episodes, "Fly Me To The Moon," was originally done by Bobby Darin (well, it may have been done by another memeber of the Rat Pack, but since they frequently shared songs, I suppose the point is moot). If you're a fan of lounge music and the like, you might enjoy him. Some of his other hits include "Mack The Knife" and "Somewhere Beyond The Sea" which (yeah, I'm rambling) played during the scattering of Mr. Scully's ashes in an early X-Files episode.