Hey RajeshKvm,
The projector may need a software and/or firmware update to ensure it stays compatible with the iPadOS version. This is a good place to start, since other devices are working as expected when using the adapter.
Another troubleshooting to help isolate the issue, is testing with a different lightning to HDMI adapter. Preferably one thats Apple branded and/or Apple certified. For information on identifying Apple certified accessories, review the information here: Identify counterfeit or uncertified Lightning connector accessories.
If the projector software/firmware version is up-to-date and a different adapter didn't help, let us know exactly what happens when iPad is connected to the projector. Does the projector and/or iPad so any error messages or alerts?
Have you gone through powering off and restarting both devices?
Let us know. Take care.