Official comment
Glad you like lyric! Two things-
You can adjust the speed of the tracks start in MS so if it comes in to slow you would speed it up and if it starts to soon you would slow it down. Go to the lyric window and click the ABC box, then click Motion and at the bottom of the screen is the DELAY COMPENSATION box where you can adjust the timing of the track in or out.
Also you can request exact versions of songs, but with remixes it can mess up if the program is based on the original non-edited version of the track. Suggesting this to Cotodama would be your best bet..