There isn't a noun here that would require the possessive, so "Michael" should not have an 's' at the end -- even with an apostrophe -- unless you have chosen a verb form that requires "is" or "has" (e.g., the present progressive or the present perfect).
2. Word confusion:
Lend and borrow: someone lends to you; you borrow from someone else. Note also that "Loan" is a noun, so you should avoid saying that someone has loaned something.
3. Verb tense:
If you construe this as a typical or repeated action, use the simple present tense ("lends"). If you construe it as something that goes on for a period of time, use the present progressive ("is lending"). If you use the present progressive, put the adverb ("always") after the auxiliary verb ("is always lending").
4. Adjective word order:
The convention for adjective word order is opinion, dimension, age, shape, colour, origin, material. This produces "stylish, sporty-looking, newer, red car" and "battered, old, rust-spotted, white vehicle". Some of you might have wanted to group some of the adjectives and combine them with a coordinating conjunction ("stylish and sporty-looking"). That’s another good way to solve the problem. Don't forget to separate these adjectives with commas.
5. Verb tense:
Whether or not the simple present or present progressive tense is used for the verb in the first clause, in the second clause, the verb (which should be "borrow") needs to be in the simple present tense ("borrows"). This means there is no apostrophe 's' attached to "who".
6. Word form:
After "for" do not use the gerund; use the basic noun in the either the singular or plural form.
Michael always lends his stylish, sporty-looking, newer, red car to his brother, who borrows it while his battered, old, rust-spotted, white vehicle is in the garage for repairs.