Lifestyle tips

I get lower back pain every time I gain 10+ lbs. For me, it’s entirely a matter of muscle strength, and that leads to poor posture, especially when I’m standing up. It’s probably safe to say I gain my weight lower on my body than your husband has on his, but in either case I’d suggest doing a few set of freestanding squats, (legs parallel to one another, arms outstretched straight in front, and bending at the knees while keeping the back straight... or just google it 🤣).
I try to do 3 sets of 8-12, depending on what I’m reasonably capable of at the time. A handful of those over a week or two tends to be all I need, and I hope it helps him!

Squats are great advice.

I'd also add stretching out the large leg muscles that can shorten (esp with sitting) and pull on the lower back. Lower back stretches need to be gentle, but building those muscles to support the weight will go a long way.

Maybe some beginner Yoga, too?

Sometimes back issues are due to imbalances or tightness in muscles. The result is that the pelvis or spine is pulled out of alignment. This can be alleviated by stretching and balanced weight training as well as core exercises.

If you look up "McGill big 3 back exercises" you should find a set of three simple excercies that can be done with no equipment, designed to strengthen all the key core muscles (developed by a doctor who dealt with a lot of back stuff, and found that in the end it was strengthening the core that made the most difference for the most people, so then he started looking to boil down the various possible exercises into an easy and compact set)

When I'm good about doing them I have no back problems, when I start slacking off my lower back starts bugging me.

short term new shoes or good insoles.

I've had back issues for years.
A good quality mattress is important.
A 30 minute walk each day helps a lot. If he's not active at all, build up to it. My orthopaedic surgeon once said he thought that walking is the best thing for your back, as you use the relevant muscles and strengthen them, but gently and thereby avoid further injury and problems.

I do yoga for back strength when I gain as little as 5lbs. It helps bring my back muscles up to snuff with my belly that weighs more and sucks out further (extra leverage against my back)