I know that the title is a little bit clumsy, so let me explain further.
From basic grammatical rules, we know that we should use "is" when "a lot of" is followed by an uncountable noun.
There is a lot of sugar in the container.
Also, we should use "are" with "many"
There are many people over there.
Then I wonder what to use if both appear in a sentence.
There _______ (be) a lot of fruit and many facilities in the museum.