It's been a while between lessons, so I forgot what we were studying.
There was quite a gap between our last lesson and this one, so I don't remember what we studied last.
この場合の「間があいた」は次のように言うと自然で良いでしょう。
ーIt's been a while between lessons, so I forgot what we were studying.
「レッスンとレッスンの間があいたので何を勉強していたか忘れた」
It's been a while between lessons .... を使って表現できます。
ーThere was quite a gap between our last lesson and this one, so I don't remember what we studied last.
「最後のレッスンとこのレッスンの間が結構あいたので、最後に何を勉強したか覚えていない」
There was quite a gap between our last lesson and this one ... のようにも表現できます。
ご参考まで！
カナダ 
