How to auto lock a cell once data is entered

The only way to lautomatically ock a cell after data entry is to use VBA.
However, users have the option of choosing to enable macros when opening the workbook and if they choose to not enable them then *ANY* VBA code is defeated.
The only way around that issue to set macro secutiry to allow macros to run without notification - this *IS NOT* recommended and most IT/administrators generally don't allow this.

To use VBA code for this you must first unlock all cells into which you want to allow data entry. Cells are locked by default.
Then you must apply worksheet protection - setting the options you want.

Try adapting/testing this basic code:
Note: sheet references in the code are to sheet code names - not worksheet (tab) names

This code must go into the module named "Thisworkbook". It allows macros to run on a protected sheet.

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This code must go into the module of the target worksheet

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Adjust cell ranges as needed.