@yuri_v_a I have the same problem now. My problem before was that the Epic Launcher cached my lyra sample download which still was UE 5.2.
After deleting the cached files I could select the Engine Version to create a new project. I now copied all the neccessary files to my project and deleted some unused ones which used deprecated functions.
Now the project runs so far but as you mentioned, the basic lyra inputs are working (for me movement also works) by my custom inputs not.
I will give an update here once I fixed these issues.