The first part of your question is exactly right: too much money, too much water, too many dollars, too many lakes.
As for "I have too much time" – by itself, that means something like, "I have so much free time I don't know what to do with it." So, I'd say that part of your question is correct as well.
The last part is where things get dicey. "I have a lot of time" (which could also be phrased as "I have plenty of time") generally means "I have a lot of available time," and that could be for any number of reasons – it's context dependent. I would think that any of these questions or comments could be answered with, "Yes, I have a lot of time":
Thanks for helping me fix this lawn mower; do you have enough time to help me fix the wagon, too? (In other words, Do you have any remaining available time right now?)
I was wondering if we could set up a meeting sometime next week. (In other words, Sometime in the future, will you have a block of available time?)
Our football team needs a treasurer for the upcoming season. Could you volunteer? (In other words, Do you have enough available time that you could take on some short-term responsibility?)
Could you take on a second part-time job in the evenings? (In other words, Does your schedule have enough free time that you could take on another activity on a regular basis for the foreseeable future?)
And then there's the context you mentioned, where the answer might be "No, I have a lot of [free] time":
- Are you so busy right now that your life is just completely hectic?
So, "I have a lot of time" can mean several things, depending on the context.