Hi Hanna,
Your assumption about the Explicit Lifting is quite correct. It is feature tied to the MAQL, concretely to the BY clause that allows you to lock aggregation on a certain level.
Unfortunately, it cannot be applied on a dataset level.
However, you can create one or multiple bridge datasets and work with many-to-many relationships in your model. Please check the article below for more details.
Many-to-Many modeling