Erm...well, depressed people don't necessarily live on anti-depressants. Some, me included, find the idea of anti-depressants 'depressin' 
Nevertheless, bear in mind - as you know - that 'wanting you to beg' is clearly a power game. And that, for some, is a way to make them feel better about themselves. Being selfish is part of the process. Also, I notice there's a significant age gap which may contribute to the problem. If you're much younger than him, maybe he's feeling frail in comparison. A defensive trick would be to force you to beg for sex. It gives him back a sense of control which - perhaps - his body isn't providing sufficiently.
I don't know your husband to formulate a solid diagnosis, but I'm basing my evaluation on your input only. Which may make my understanding incomplete, if not distorted, of the situation. So, please accept my apology if I crossed the line with me 'presumptuous' inputs.
If you think he's too lazy to have an affair, then you really need to reconsider. An affair doesn't have to be physical. In fact, he might be very immersed into his thoughts so much so that the became fixated on that 'fatansy', person, or problem. Of course, I'm not saying he's probably having an affair, just pointing out other possibilities (not mansplaining, by the way 
).
Anyway, try talking to him. And be gentle, don't 'nag' or otherwise he'll run for the hills or shut down completely. Men are big children, really big children who sometimes need a 'mummy' figure to take their hands. There, I let the cat out of the bag!
If sex is still an issue, ah, well...I'm available - but seriously, gauge him as much as you could, you never know what you might find out!