Both expressions would be acceptable and easily understood. "There are a lot of people in the room", would be the more formal and proper expression. You could also say - "There are many pieces". "There are plenty of parts" "There are a large number of businesses." The expression, "there are lots" might be questioned by your English teacher if you wrote it in an essay. It might not be the thing to say during a job interview. Hope this helps

There are a lot of people. The moment you put a before lot you dismiss lots. Also, a failure I used to do was "There is a lot of" or "There are a lot of" In that case, you have to figure out what can be counted and what not. If it can be counted than there are (like issues, problems, people) But if it is something uncountable than there is a lot of (water, fire, etc.) To make it sound more smooth use "plenty of" instead of a lot or lots of.

They're both correct though "lots" is considered even more informal even though both are informal. People seem to argue over this considering that "a lot" can also mean a particular grouping of a thing, but I really think the distinction is almost nonexistent other than the subtle effect of "lots" sounding more childlike.

But I was surprised when I heard 'there's many/there's a lot of...' instead of 'there are...'.

Accidentally sent two.