It's a "give & take" kind of relationship when trying to put on lean mass.
Training for strength and muscle mass are two different types of routines.
Strength requires heavy loads for low reps and building muscle requires things like VOLUME (higher reps) and a slower TEMPO.
But like you, I don't want to lose strength while building muscle so I have been incorporating 5x5 training into my current workout split to help even things out.
Think about it this way... when trying to build muscle the "weight" doesn't really matter up to a point. Whatever you are lifting just needs to be heavy enough to fatigue the muscles by the time you hit around 12-15 reps. So what I have been doing is including at least ONE 5x5 lift in each routine to focus on building strength. Then while fatigued, I finish off the muscles I am training for the day.
Here is an example for each bodypart:
Back: Weighted Pull-Ups (5x5)
Chest: Barbell Bench Press (5x5)
Biceps: Straight-bar bicep curls (5x5)
Triceps: Close-Grip Bench or Weighted Dips (5x5)
Legs: Squats (5x5)
Traps: Shrugs (5x5)
Shoulders: Barbell Overhead Press (5x5)
What also works great about this type of training is that the muscles are now pre-exausted which means more muscle fiber activation during your workout.
After completing the (5x5) for the bodypart(s) I am training or the day, I go into my normal workout split and hit it as hard as I can.
Try it out and let me know what you think Nation! #HTH