There does not exist a lagless converter either for PS2 -> 360 or 360 -> PS2.
EDIT: I just saw this on SRK
Max Shooter by Mayflash: This is the best option for using a custom stick on your 360. It works great with Sony controllers. Be certain that you can tell it apart from the XFPS because eBay sellers often label these incorrectly. Unfortunately it has issues with the HRAP 2.
Compatible with: PS1 Digital, PS1 DS, PS2 DS, HRAP 1, SFAC 3.5V, SFAC Pad, Saturn PS2 pad, Namco PS1
Incompatible with: HRAP 2, SFAC 8V
Review: http://forums.shoryuken.com/showthread.php?t=189236