If you want to get lean while lifting, your strength numbers will go down. There's no getting around that fact. The body is always either in an anabolic state or a catabolic one. If you're OK with getting weaker in the big lifts in exchange for a leaner body, then the main thing you need to do is to count your calories like a Jew counts shekels and up your protein intake on your lifting days, while keeping the weekly calorie count lower than your daily baseline average (TDEE). Eat a lot less on days you don't train, but eat slightly more on days that you do.
You'll see results in as little as three months, but give it around six for some room to observe effects and make any needed changes.