There are a few phrases that you can use, such as in place (of), instead (of) (also stead), to express the "doing something for somebody", depending on the context.
In any case, the phrase for someone doesn't have to mean that the person you do something for must be lazy. This, again, depends on the context. Compare:
He asked me to do his assignment for him.
I offered myself to do his assignment for him.
Here are some examples of in place (of), in someone's place, instead (of), and stead, I found on the web:
John came to help in place of Max, who was sick.
When the king's cloaked challenge is answered, Fluellen stands in place of him, representing him, and receiving the blow.
She knew she should not have sent him to work in her place tonight.
"O king, take my life instead of hers. Let me die in her place," he pleaded.
... it was Judas who was crucified instead of him, ...
... she had to ask their family doctor to prescribe instead of him making it available to begin with.
Take me instead! Not my boy!
The chairman spoke in her stead.
The marketing manager was ill and her deputy ran the meeting in her stead.
So, you can say any of these followings (choose wisely, register is important),
He asked me to do his assignment for him.
He asked me to do his assignment in place of him.
He asked me to do his assignment in his place.
He asked me to do his assignment instead.
He asked me to do his assignment instead of him.
He asked me to do his assignment instead of him doing it himself.
He asked me to do his assignment in his stead. (formal)
It's not common enough to be an idiom, but I've heard the expression, "getting paid to eat ice cream", though only in the first person and only concerning employment. So,
"Did you hear? I've been offered a field job!"
"You always did like travel."
"I know, right? I'm getting paid to eat ice cream."
The origin may be a quote from musician Bob McQuillen, the biography of whom is titled "Paid to Eat Ice Cream", after something he said about being a professional musician.
You know, it sounds like your language has a very handy idiom there, for which there's no direct English correspondence. English being what it is, if you shared the literal translation, it might rapidly become an English idiom.
Best Answer
It sounds like you're asking two different things. There's a general expression to indicate that everyone experiences some misery in their lives, and then there's an expression you'd use as a comeback to the person you mention above.
As a comeback:
As a general philosophy: