Not Cathe here, but as one with knee issues, I'll give it a shot. First is it PAIN or is muscles that are tired or sore. If it is just tired/sore/not strong enough then the lunges/squats are prob what you need to be doing to strengthen them. If it's actual PAIN, I'd start with seeing a Doctor for the cause. Knee issues can be tricky to diagnose or there can be more than one thing going on (as in my case). I've had 2 knee surgeries and here's what I've learned--
If the supporting/surrounding muscles are weak, then your knee will be wobbly and it will hurt. The surrounding muscles have to be strong, stable. Try leg lifts in all 4 directions, also band work in all 4 directions. Firewalkers are good for the inner/outer muscles as well.
Your balance has to be good. Ties in with the supporting muscle thing. Try balance boards or an upside down bosu. See how long you can just stand. Then progress to squats. For squats keep your weight in your heels/but. Try lunges on the bosu. Put the forward foot on the bosu and push up thru the heel on the forward foot, the back leg is mostly for balance. For either exercise, your weight should not be center on your knees. They are not bearing the weight. Let the muscle do the work, not the joint.
You have to maintain focus/concentration. My inside leg muscles are weaker than my outside, and that pulls my knees to the outside, which then my kneecap doesn't rub right, and I no cartilage behind my left knee. It helps during these exercises if I really focus on bringing my legs back to "center" and not letting them roll outward. If yours roll inward, focus on them being out. If I let my form go sloppy then I am soooooo sore the next day - in a bad way. Also for this, step up and over a step. Get a comfortable height step, start low then work up. Put your right foot on, then step up and over, then back with your left foot, but do not lift up the right foot. It puts a good stretch in the hip and kind of mimics a lunge move and requires strength and a lot of stability in the planted leg. Repeat on the other side.
Do what you can do!!! If you can't go all the way down, you are still working. Quality over quantity. Since my 2nd surgery I can't bring my left knee down as far as the right. It hurts, but its not a "bad" hurt. It more of an itchy/stretchy/uncomfortable feeling where the muscle is still trying to heal and become accustomed to its new position in life. Every few workouts I push it just a little further and its coming along. But again, its the good pain, not the something is wrong pain.
Also, maybe your weights are too heavy. Perfect your form/balance/stability with little or no weight then go up. I also find that the weight position makes a huge difference. I can easily squat 50 lbs on a barbell, but if I use 2-25lb dumbbells on my shoulders all of a sudden it feels so much heavier. It throws my sense of balance and center off and all of a sudden its a much harder move.
Its possible you just need to tinker s bit with what you're doing. But I would still see a Dr to rule out any serious issues 1st. That was meant to be my .02 worth, but from the book I've just written, it looks more like $1.50
Nan