Some people are careful about what they eat and they lift weights so they don't have to rely on medicine.
この場合、次のような言い方ができますよ。
ーSome people are careful about what they eat and they lift weights so they don't have to rely on medicine.
「ある人は食事に気をつけ、筋トレをするので薬に頼らなくてよい」
to be careful about what they eat で「食べる物に気を付ける」＝「食事に気をつける」と言えます。
または to maintain a strict diet「忠実な食生活・食習慣を維持する」＝「食事に気を付ける」
ご参考まで！
カナダ 
