It's a bit confusing, but with "there is/are", the number generally agrees with the item in question, rather than the quantifier "a lot of", which you might have thought of as singular. So it's usually "there are a lot of dancers" but "there is a lot of money". You can also use "lots of" instead, which means much the same but is perhaps just a bit more informal, and it works the same way. One way to keep it straight is to figure out what it would be without "a lot of" (or "lots of"), and use singular or plural accordingly. Or mentally substitute the synonyms "much"/"Many" which don't look like nouns as "a lot" does.

You can never say 'There's lot..' The following are possibilities: There's a lot There are a lot There are lots There's lots Some people use a singular verb to agree with the singular 'lot'. It's more informal, but acceptable. It's OK to say 'There's a lot of good dancers'.