If I had been a little more familiar with the context of his life, I might have understood how he felt a little better.
context around ではなく context of... と言った方が自然な感じで良いと思います。
ーIf I had been a little more familiar with the context of his life, I might have understood how he felt a little better.
「彼の生活状況をもうちょっと理解していたら、彼の気持ちをもう少しわかっただろうに」
ご参考まで！
If I had understood the context around his situation, I may have been able to understand his feelings a little bit.
ご質問ありがとうございます。
*Context around*を使うことは出来ると思います。
"If I had understood the context around his situation, "＝「もし私が彼の状況の背景について理解していたら」
"I may have been able to understand his feelings a little bit."＝「私は彼の気持ちを少し分かったのかもしれない。」
ご参考までに。
カナダ 
アメリカ合衆国 
