I think it depends on what you are meaning to say. Lift and raise can be uses in different ways. For example,
1) Do you need a lift?
is equivalent toâŠ.
Do you need a ride?
2) Can you help me lift this box?
is equivalent toâŠ.
Can you help me pick up this box?
3) My promotion includes a raise in salary and a new position.
is equivalent toâŠ.
My promotion includes a salary increase and new position.
4) May you raise the blinds?
is equivalent toâŠ
May you lift up the blinds?
These are examples, but âraiseâ and âliftâ can have several meanings depending on how you use it in a sentence.
Does that make sense? Iâm not sure if I am being clear.