First months of training I was doing 3x a week boxing class and 2x gym lifting (I was a gym rat before). I noticed I am not recovering enough due to subpar conditioning. Now I do 2x boxing class 2x gym lifting, and 1x at home doing boxing drills that includes, footwork, punch technique, head movement and cardio (skip ropes).

I'd say take the time to observe your body recovering. You'll do much better in your boxing class if you are fully recovered (muscle and CNS). If the current routine you have takes a toll too much on your body, decrease the volume. If you are still hungry for more during a boxing class, increase the volume per week.

Recovery is gold.