From LilyPad settings try disabling "Start with mouse focus" and "Always Hide Cursor"
Both of them are already left blank in pad settings and the cursor problem still occurs.
Hmm...those are just random idea now.
1.Config=>Emulation Settings=>GS Window=>disable both vsync options
2.Try using the default mouse cursor(if you are not using it)
Both vsync options are not enabled, and I'm currently using default mouse cursor.
Hmm,no idea then,it works fine here...in fact the mouse cursor is always visible(over the game window while game is running(window and full screen mode)and it stays visible when I press Esc