I don't think there is a connection to Gano's Squadron. I think they just happen to be filed together with Lane's Regiment.

Capt Jack Waterhouse was captain in Lane's in Louisiana. Do you have access to Fold3.com? If so, look up Jack Waterhouse in Texas 1st Infantry (2nd Infantry) and read through the pages. There are several showing him in Crump's/Lane's Regt.