Injured Knee Lower Body Resistance Training?

I'm not sure where your pain occurs, but I'm just recovering from a fractured kneecap and I was pretty limited in what lower body exercises I could do. I pretty much just stuck with Romanian deadlifts, good mornings and straight leg extensions while I was recovering. I can put more weight on it now, but still having to go lighter on squats/leg press and seated leg extensions. I don't even what to think about lunges yet. So basically, try more hip hinge movements rather than knee.

I have had ACL replacement surgery and have a torn meniscus.
I am not sure I am the person who should be commenting because I honestly believe I have helped my knee to heal with regular running...But
That said, somebody mentioned box squats and the leg press machine. I think when you have a knee that hurts -- a knee you instinctively protect -- you do yourself a disservice doing bilateral exercises. You are going to favor the uninjured knee anyway, and your injured knee is going to get weaker, just with daily activities and your hiking, etc.
I stuck with mostly single-leg exercises as I eased in to my rehab and recovery.
I did lots of yoga early on, because there are single-leg poses that you just hold -- an isometric exercise (no pounding or uncomfortable movement) that kept my injured leg engaged and helped to maintain its strength.
Then I walked stairs, progressing to running stairs. (That's a one-leg-at-a-time movement, of course.)
Then I started doing box step-ups, in time, as my knee improved, adding dumbbells for extra weight.
I don't know if that helps to answer what you are asking or what. But I hope so.
I really found that the yoga poses -- and other isometrics like wall sits -- were quite helpful in maintaining the strength in my injured knee when movement was painful.

I had a shoulder injury last year so frankly, focused on squat and deadlift. If you can't do legs without knee pain- go crazy on your uppers. Go see a doctor about the knee. I had an MRI on my shoulder but it didn't help except it told me I didn't have a rotator cuff tear (was glad to at least rule that out). I kept trying to rehabilitate my shoulder via lots of light dumbbell laterals and stuff like that. It wasn't until I gave my shoulder months of rest that it actually got better. I know, this is contrary to the whole PT thing. I thought I could rehabilitate it but it turned out the only rehabilitation happened when I quit aggravating it... took months of rest.

Some soft tissue injuries will never heal on their own- the reason you should start with a consult by a doctor. Rule this possibility out first.

The good news is you just got a partial pass on "leg day". In my case, my squat went through the roof during the months where I was not able to bench press or press- due to my shoulder. Sometimes you have to just work with what you got. Sounds like you can go crazy on uppers while you baby your knee. Could be worse.