Sleepy while feeding

Does anyone have suggestions for getting my baby to take a full feeding without falling asleep before she is finished!? I saw an LC and she did mention she might have a tongue tie and lip tie, and we haven't done the procedure, but I don't feel like this is the entire problem. She will eat for a few minutes and fall asleep but then won't be able to stay asleep because she hasn't eaten enough and then this cycle lasts all day sometimes!