Can these negative effects be countered/offset by continuing weight training? I lift 2-4 days a week.

Yes, but you would certainly still see some - it's just a consequence of weight loss. Even IFBB bodybuilders on god knows how many steroids see some muscle loss when cutting.

Eat a whole lot of protein, lift, and you're going to be doing more than fine in the muscle loss department.

Certainly, just like with any other diet.

I gained muscle mass by doing strength training 2 times a week while on GLP-1 drugs.