a thought occurred to me
彼がうそを言ったのかもしれないという考えが私の心に浮かんだ。
It occurred to me that he might have been lying.
よい考えが私の心に浮かんだ。
A good idea came to me.
突然良い考えが私の心に浮かんだ。
A good idea suddenly occurred to me.
そのとき良い考えが私の心に浮かんだ。
Then, a good idea came to me.