Validity of AWADDR once AWREADY is asserted in AXI4-Lite interface
No. When AWREADY is asserted with AWVALID high, AWVALID must be deasserted on the next clock edge, or the other signals must be updated to reflect the next transaction. With AWVALID deasserted, AWADDR can take on any value. You cannot rely on the value of any of the AW* signals after completing the handshake by asserting AWREADY.

A module that assumes differently will then depend on the specific implementation of whatever component is upstream, something which could lead to hard to find bugs and compatibility issues. I also think it is a violation of the spec to do something like that.

You have two options here: either store the value you need and complete the transfer immediately by asserting AWREADY, or hold off on asserting AWREADY until you no longer need the value.