No.
Unless it’s the guy who dresses up in just a thong and goes and flexes in front of the mirror, in which case, hell no.
This would be so inappropriate in a U.S. men’s locker room, I can’t imagine someone asking. It would need to be a medical emergency before I’d consider it. Even with a severe sunburn, I’d figure the guy could find someone he knew.
It’s not so much that I’d mind doing it; it’s that any normal person would know it wasn’t an appropriate request for a stranger, so something isn’t right with the guy or his reasons for asking.
Even in a woman’s locker room it would be a very strange request. Even if a friend instead of a stranger asked you to do it.
Let me say what every guy is thinking: Not only would none of us do it, but all of us would be very put off just by being asked. It would be near impossible to not take that request as a sexual come-on.
I would also assume some sort of flirting. That’s just the context I know it in: some girl asks the guy to put lotion on her, or sometimes vice versa.
Since I would not want to lead them on, I would say no.
It depends
Anecdote:
In the mid-1960’s, when I was in Junior High School in Los Angeles (all the boys showered together in P.E. classes in those days), any such request would be utterly unthinkable!
Fast forward one year: My family packed up all our bags and moved to Honolulu, Hawaii. There, in 10th grade P.E. class, I found that the boys there routinely asked one another to scrub their backs with soap in the showers – it was a totally unremarkable thing to do.
That took me a while to wrap my mind around. I participated in that a few times, but I was never very comfortable about it.
Why the hell am I in a locker room?
A friend? Probably, and in fact I think I have.
A barely known acquaintance? Possibly.
A stranger? No.
I wouldn’t expect it done to me by a stranger either.
Well, in that case I’d do it. 
But I’d let him know that I’m married.
Medical emergency, the fuck? I’m not heartless, I’d offer to call an ambulance.
“The backstroke.” <canned laughter>
Or the breast stroke.
I’d do it, and wouldn’t think twice about it.
There is a strange woman in our gym who likes to spread lotion on the backs of others without asking. That’s a bit more weird.
That’s the “If a stranger approached you in the locker room, and asked you to urinate all over his/her body…” thread.
Dear Penthouse Forum…
What is a “locker room”?
No.
Sure. There is nothing skeevy about (most) people’s backs. I’d do it for anyone on the beach who was having trouble with their sunscreen or lotion, why not in a locker room?
I too would not want to touch a pretty lady.
I grow my own locker rooms at home and they are much tastier than what you can buy at the store.
Funny. I’m a firm no on this, but am okay with kissing a dude (at a price) for the scavenger hunt lady in the other thread. I’m guessing because in that case I’m assuming me and the other guy wouldn’t really want to do it, but $50 is $50. Some strange guy asking me to lube him up is completely different, for me, apparently…