Positive Photo Resist for lift-off & Negative for EBL?
Let's clear up some terminology here for the benefit of the reader.

A positive photo resist is one in which the exposed areas are removed in subsequent processing steps. i.e. where ever the light shines, the photoresist (PR) is removed.

EBL means Electron Beam Lithography.



In lift off, you are depositing a layer of material on top of a PR layer, there is subsequent processing that removes the PR and in that process "lifts off" the deposited material along with the PR.  In places where the PR does not exist the deposited material adheres to the exposed areas and remains after the PR processing.

In EBL your patterning is through electrons, and when the electrons impact the PR they cross-link the polymer making it harder.  That means in areas where the beam contacts (is exposed) the PR stays behind.  It is possible to make a Positive EBL resist but the mechanism for exposure is one of damage to sensitize to subsequent processing.  This is difficult to do without also damaging the substrate.