a lot of / lots of

a lot of / lots of
嗯
There is a lot of water.
There is a lot of books.
There are lots of books.
There is lots of water.
这是我的猜想.
这里的there be句型中的be 是根据a lot of、 lots of 的变化而变,还是根据后面那个名词的变化而变?
如果说根据a lot of、 lots of 的变化而变,那么 a lot of 时用is lots of 时用are
如果说根据后面的名词的变化而变,那就是不可数用is 可数用are?