I would even go so far as to say, aside from transferring your luggage yourself, I would ask Bell services at the resort you are transferring FROM to hold it at the resort and then Lyft over to your new resort with your luggage only after your room is ready. That way you can take it directly to your room yourself. Ask your Lyft driver to drop you off at the building of your new room if possible.
Why?? For example I have been reading reports that Luggage is a mess at Pop Century and sometimes they just can't "Get to" your luggage delivery until very late, if not the next day. I believe that at certain resorts luggage is being outsourced to a 3rd party that is not doing a great job delivering it to your room in a timely fashion or is "losing" it temporarily. Another report that I read said that when a guest tried to pick up their luggage they were told that it was buried in the "Back" and they would have to wait until the staff could "get to it".
Welcome to the new emphasis on Disney Customer service. Expect more and more of this kind of thing as resort rates sky rocket and value, amenities, and customer service decreases.
~NM