They could mean the same, but they could also be quite different. It depends on what you mean, and what the person you're speaking to already know about your feelings. Remember, there are at least 2 types of love: romantic and platonic. (There are also other types of love, such as the love a parent has for a child, or the love that a boy has for his dog.) Just considering the first 2 types of love I mentioned, you want to make sure you don't send the wrong signal. So, for me, "I love her a lot" would signify a romantic love: "I can't get her off of my mind." "I want to spend the rest of my life with her." "I've never loved another woman like this before." Whereas, "I have a lot of love for her" sounds platonic, or even less. "I have a lot of love for my friend." "I have a lot of love for my team's star player." "I have a lot of love for him", (who you don't really know, but his political thoughts are exactly like yours). This type of usage is actually becoming more common among younger generation. There is some crossover, and depending on the situation you could make yourself understood. For instance, you could tell your friend, “I love her a lot” referring to you’re favorite singer, while you’re at her concert, and she also happens to be your friend’s favorite singer. He’ll probably know what you mean. However, you need to be careful. If you say, “I have a lot of love for my sister,” that would probably be understood, and would be OK. However, if you say, “I love her a lot”, that might make things awkward a family gatherings.

The second sentence is unusual and uncommon, but grammatically correct. Other than that the two sentences are the same.

The second option definitely sounds more formal. The meaning is same, but I’d expect to encounter this kind of sentence in a book, not everyday conversation

I think the idea is the same.....