Well, a few thoughts.
First, the changes on the surface of the skin may be unrelated to the the lump beneath.
So, first, I would focus on the lump. It could be anything from a cyst, nodule, mast cell tumor, lipoma (fatty deposit), etc...
So, under these circumstances, I normally start with a simple fine-needle aspirate test.
A fine-needle aspirate test is performed usually without anesthesia and is very quick. Your veterinarian takes a few needle samples from the lump (the needle is no larger than the needle used to give vaccines). The sample is smeared on to microscope slides and submitted to the laboratory. It is not always as definitive as a biopsy (this is a full tissue sample), but often it can yield enough information to determine if it is anything to be worried.
Fine-needle aspirate test
That will give you a working idea if there needs to be concern about the lump.
The skin may be a completely benign change, no different than a mole, skin tag, blemish that occurs with time on a person.
Also, I wouldn't be against suggesting you ask your vet for a referral to a veterinary dermatologist for the skin change.