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No,in the library they dont specify the LUT corresponding to a particulat gate.
Instead its only the change in value of the memory element present in the LUT.
Like a lut of 4 input can have 3-1's and a 1- 0 will behave as a 2 input OR gate
the same LUT with 3-0's and 1-1's will behave as a 2 input AND gate
FPGAs not only have LUTs but also basic AND/OR/XOR etc. gates, depending on the vendor, model etc. Take a look at this article for more details. (If you also take a look
at an FPGA STA report you will see that gates other than LUTs are present with much smaller delays).
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