Below are some leagues that have lacrosse games for a set schedule.  The leagues will usually take individual players and/or a group of players and keep them on the same team.  Depending upon the league, there may be limited practices.  These leagues present a good option for a player to develop their game skills.

Ath-Ed Sports

https://sites.google.com/site/athedsportsinc/leagues

Primarily games for all levels

The Lacrosse Academy at FDU

http://www.thelacrosseacademyfdu.com/

Springfield Lacrosse

http://springfieldlaxnj.com/

Springfield lacrosse runs a summer league for U8, U9, and U10.  It includes both practices and game play.  It is open to players from other towns.