The phrase "not a lot" emphasizes that while there is some, it's not a huge amount. I don't have a lot of money saved up. I don't spend a lot of time window shopping. Yes, there is some, but not much. It emphasizes that it's not a large number.
Of course, all these things are relative. If a millionaire said "I didn't spend much money on this necklace" and it was $12,000, the statement would seem odd to me.