In that case I would expect no glitches, or at least for your logic vendor to tell you how to implement it to have no glitches. That's not the case for your original question which involved two inputs changing at the same time. In your original question, any asynchronous logic type can have glitches.
It's not automatic, a LUT is not identical to the logic gate it replaces. It's actually a multiplexer, and multiplexers can have switching transients. So it is certainly possible for a LUT implementation to have glitches even when a single input changes, but FPGA chip makers should try to prevent that because it's important for a many important FPGA primitives. For instance it's common to implement clock domain crossing of e.g., FIFO pointers using grey codes so that only one bit changes at a time. The LUT architecture needs to support that without creating glitches.