In a common scenario, some individuals are unable to squat because of lower-back problems. However, they still aim to add some size to the thighs, but the only exercise they find they can do without hurting the lower
back is leg extensions. However, there is a common myth that leg extensions will not add mass to the thighs. Is this true? Let's take a closer look.
Leg extensions can add some appreciable size to your quads, but certainly not to the extent that barbell back squats can. Although you say to keep from hurting your lower back the only exercise you can do is leg extensions, my gut feeling is that you could also do 45-degree leg presses and as a finisher, barbell front squats and/ or bodyweight-only sissy squats. Certainly check with your physician first to ensure that your back doesn't have any major problems.
You didn't mention any existing knee problems, but to safeguard against future knee injuries, I suggest that before your leg workout you warm up your knees with five minutes on the stationary bike and then do some quad stretches. When you're fully warmed up and stretched, you're ready to begin what I call the "no-barbell squat workout." Basically it consists of a tri-set of the three exercises mentioned above.
Begin with leg extensions in a two-part movement. Do the final 25-degree top range (i.e., the top quarter of the movement) for 20 controlled reps, making sure to tense your quads maximally as you lock out each rep. Upon completion of the 20th and final quarter-rep, lower your legs all the way down and then immediately do 20 full-range-of-motion reps. The lactic acid burn should be almost unbearable. Your quads should feel as if they're being blow-torched.
Without any rest whatsoever, walk over to the 45-degree leg press and do 20-30 reps, lowering your legs all the way down until they touch your chest. Then push your legs up to just shy of lockout (for maximum muscle tension). After the leg presses immediately begin pumping out 20 full reps in the bodyweight-only sissy squat. I would go with the barbell front squat. Do three tri-sets as described. Your cardiovascular system will demand 3-5 minutes to recover from the rigors of each tri-set.
As with any exercise program, you must not only train hard but also train smart. Some bodybuilders overwhelm the ACL (anterior cruciate ligament, which crosses over the front of the knee) when doing leg extensions, so proceed with caution. Perform all the reps in a smooth, continuous manner.
Take care on the 45-degree leg press that your back is flat against the seat back and that your glutes also stay flat, especially in the bottom position of the rep. And don't curse me when you're working through the pain barrier of the three tri-sets. Heck, I learned about this no-barbell squat workout back in the '70s from a top California champion bodybuilder named Dan Howard. Give it a shot.