I have done this in the past and I am in the process of doing extensive revisions so expect to be doing it again, so here's my two cents.
In general, I agree with Nathan Bransford here:
https://nathanbransford.com/blog/2019/06/how-to-work-with-a-literary-agent-on-edits (section titled Should I send an agent my revised manuscript?).
Now, the key point is whether the changes are substantive enough.
Earlier I asked an agent if I could send a revised ms and she said yes, but she's completely ghosted me since. The changes, sadly were not substantive (although I thought at the time they were). Now that I am making truly significant revisions, I realise what Nathan means. So unless you are absolutely certain there will be no other major changes to the book, don't send it. In other words, don't burn your chance with the agent when the changes don't truly alter the book in a major way. If they do, and you have no intention of changing anymore, then yes, I for one think it's worthwhile to say something like, "I've received some great editorial feedback and I've reworked my novel extensively, and would you like to see the new version?".
Now speaking of fibs and tactical omissions, I wouldn't mention it was a beta reader who gave me the editorial feedback and let the agent assume it was another agent/editor/someone grand.

Good luck!