If you want more of a furniture piece in your portfolio choosing a lamp isn’t a bad idea.
They can be fairly manageable project but still refined and impressive.
On the other hand, I wonder if it is too broad and if you should chose a specific lamp to “re-skin”.
To me it sounds a little bit more as if the assignment is looking for a “before-after” type of result. With lamps this is really difficult.
I would say that building a strong story and POV will be important here so it doesn’t feel like “just another paper lamp” by a student but that it has true purpose beyond its esthetics. What are the reasons for a re-skin?
A lamp that is in the line up you posted and is a good example of a successful re-skinish kind of project is Grcic’s Mayday lamp.
He created a high-end product with a very exclusive manufacturer (Flos) but had a truly utilitarian approach and language to the design.
In the promo material, you see the lamp being used in a variety of workshops such as autoshops and garages.
I happen to actually use it both when I am working on my bikes in the basement and when I am reading in my bed. I find the synergy inspiring and it tells a great story in its versatility without feeling insincere.
So my advice would be to find a use-case and storyline you can ground your project with and then the form and function will make sense.