What I know is this is an idiom and its origin is from Zhuangzi, a Chinese philosopher. He said, "the clever toil on, and the wise are sad. Those who are without ability seek for nothing. They eat to the full, and wander idly about." (from the Sacred Books of the East). The meaning is to praise a person who is capable of doing many things well and therefore he/she is always busy because he/she is always in great demand.

it's a set expression, kinda 成语, means "nice guy works much"

I don't know whether it is a motivating one or a sarcastic one,because it depends on who made it.I'll explain the meaning to you. 能 capable 他是个能人（he is a very capable person. ） 者 person 学者（learned man） 多 a lot or more 你应该多吃点。（you should eat more.） 劳 work 好逸恶劳（loves luxury but hate to work） The whole sentence means A capable one needs to do（work） more. So，if it is written by himself he approves himself，but if another people put this on the door，may be sarcastic，may be not，it depends.

能者多劳 is laudatory or complimentary. Dictionaries give definitions for it like this: able people should do more work. You use it in such contexts: 1) You are encouraging or pushing someone to take a (maybe extra) job by giving he/she this praise. 2) Someone is complaining to you (maybe being a leader or boss) he/she has (being) done lots of work while getting less reward or recompense. You say this to soothe him/her.

I think it's similar to "great power comes with great responsibility". basically means that capable men do more /challenging work