Quick question, are the brushes in a brushed DC motor supposed to be lubricated?
No, the lubrication would either insulate or short what it should not.
This answer only applies to graphite brushes which are the most common type.
No, you don't need any kind of extra treatment for them. Professional power tools all use motors with graphite brushes and the only maintenance they need with respect to brushes is having the brushes replaced once they wear out.
Here's a curious detail about professional power tools that only supports the fact that no extra treatment is needed. A tool comes with "hard" brushes that live approximately 100 hours (total time of motor being on). The replacement brushes are "soft" brushes that live approximately 50 hours. The difference is that "hard" brushes are meant to fine-polish the motor collector but if you use them as replacement they will polish it too much and wear it down beyond repair. So you run the new tool with "hard" brushes, they polish the collector during a kind of break-in period, then they wear out and you switch to "soft" brushes for the rest of the tool life. Both "hard" and "soft" brushes slowly wear out and the peeled off graphite acts as a lubricant.
Don't add any, it will interfere with either the electrical, or mechanical properties. The brushes breakdown and produce their own lubricant (a fine graphite powder).
I had two micro dc motors, both were squeaking like in this video:
and as the guy shows there, a tiny drop of oil helped them a lot also in my case.