The penis (as opposed to the upper, real brain, which is located in your skull). Used as a metaphor for male sexual urges. "Thinking with your lower brain" is the act of discarding all logic and sense (apparently the job of the upper brain) in order to gain the affection of/have sex with the opposite sex.
Horatio: Sure, Clarissa, I'll go skinny-dipping in highly-concentrated sulphuric acid with you this weekend.
Algernon: Stop thinking with your lower brain, Horatio.