"Put on light music" (No comma) It means to begin to play music on the radio, CD ... "To put up an umbrella" is correct when you open it to walk in the rain or to use it as a sunshade. "To hand an umbrella" means you hang it up on a hook when it is not being used.

"Put on light" sounds very strange - I don't think you should use it. If people said it, it would mean "turn on a/the light(s)." "Put on music" means "start playing music" and it's perfectly normal. "Put up an umbrella" does mean to "hang up an umbrella." For example, I was talking with my friend, but he was busy sending messages from his phone. I asked him to put his phone up and he turned it off and placed it in his pocket. Which dictionary do you use? I highly suggest using the Oxford Learner's Dictionary series (it comes in both intermediate and advanced versions). Here is the online advanced version: http://www.oxfordlearnersdictionaries.com/ This dictionary shows you how to use common phrasal verbs and their common collocations (words which usually go together).

I suppose "put on lights" is a expression used to light a candle in a romantic dinner or some similar situation. "Put on music" means to play some music. Put up an unbrella is a very uncommon expression. I'd rather use "Open an umbrella". I hope I was helpful.