English Translation
Let me do that for you.
How does the prepositional phrase get the final position, rather than ‘tun’?
If this isn’t wrong, it’s at least very unnatural.
I imagine the author wants to emphasize that he/she is doing it for the wellbeing of the other person. For example,
- give her/him a massage
- babysit the children so that she/he can finally go to the yoga class
The delivery man can carry your new washing machine up to the third floor (instead of you doing it), but that’s not really for you, just instead of you, if that makes sense.
The normal way to say it, is what you expect: “Lass mich das für dich tun!”
Now imagine this scenario:
The father says to his daughter “I can babysit for you so that you can go to the theatre.”
The daughter replies: “Oh, that’s sweet, but you don’t have to do that. You have so much work to do.”
The father insists: “That’s fine, I’ll do the work some other day. You deserve a free evening. Please, lass mich das tun für dich.”
“Ok, if you insist.”
That’s the only scenario I can imagine where it doesn’t sound wrong and/or unnatural.