Unfortunately, your reasoning is wrong. Nevertheless: 1. There aren't any lobster = zero lobsters (not any = zero) 2. There are no lobsters = lobsters are missing from the table (or the river), when they shouldn't be. Compare: There's no hot water today. There's no electricity. I had no internet connection for 2 hours yesterday. None of the above can be expressed with "not any".

"there aren't any lobster" is colloquial speech and is not accepted in formal writing. "There are no lobsters to be found" (or "There is no lobster to be found") is the correct usage. To make things more complicated, note the following singular forms used in these sentences. "No one under 21 IS allowed entry into this establishment" "DOES any of these biscuits taste funny to you?" "Any taker for this job?" "No lobster under one pound may be removed from the ocean".

so can you tell me what is the diffrent between "there is no" and "there is not any"?

I think both of them are right

You are probably analyzing this too much! :) "There aren't any lobsters" and "There are no lobsters" are both correct and mean exactly the same thing. In my opinion there is no difference in meaning at all between the two sentences. Of course, as stated in the answer above, "There aren't any" and "There are no" must be followed by a plural noun. So you can't use them with singular nouns or uncountable nouns like water and electricity. I hope this helps!