Note that you are using "lassen" in two different ways here, once inside an idiomatic expression ("außer Acht lassen" - "to ignore") and once in its usual meaning ("ihr die Aufgabe lassen" - "to leave the job to her"). Using "lassen" only once in this context constitutes what is known as **Zeugma** or **Syllepsis** ([wiki link](https://en.wikipedia.org/wiki/Zeugma_and_syllepsis), lood at Type 3), and while Wikipedia apparently decided that that sort of thing is generally grammatically correct, it does sound _very_ unnatural.

Saying it twice also sounds odd, since using the same word in the same position twice also sounds odd. The most natural way would probably be to find a formulation that expresses one of the two parts of the sentence differently.

In cases where you use the word the same way in both cases, it will be more natural to only put it once, e.g.:

> {Pointing a gun}: Ich ersuche Euch, mir Eure Geldbörse, und ihr Euren Gehrock zu lassen.

But you can also just put it in the first time:

> {Pointing a gun}: Ich ersuche Euch, mir Eure Geldbörse zu lassen, und ihr Euren Gehrock.