There are a lot of apples on the table.
The verb must match the subject, 'is' is the singular form, 'are' is the plural. To test what is correct try moving the subject around.
There are a lot of apples on the table.
A lot of apples are on the table.
This particular sentence can be confusing because it looks like 'lot' could be the subject, as if a 'lot' of apples is a particular number, but saying 'a lot' is like saying 'some'.
There are some apples on the table.
Note:
Many times the usage of the verb 'to be' is determined by the way it sounds in speaking .
If it was more like speaking an American would say "There's lot
s of apples on the table." putting the 'is' right back in there.
So, in your original question, ignore the 'lot' and watch your apples.
Joe