Downsides of showing email address on Android lock screen
Your email address is generally public knowledge, so disclosing it is often not a big security risk.
But it gets complicated when it's your phone. Because your email address is often used as your username to log into services, and you (should) use your phone as a second factor when logging in, tying those two pieces of data might have unintended consequences. Yes, you (should have already) encrypt your phone and you (should) have a strong password to log into your phone, but there are risks depending on how you implemented everything.
The better option to do what you want is to display a secondary address that you do not use as a username anywhere. This is easy to do and to simply forward all emails from there to your primary address.
If the goal is to allow a sincere finder to contact you but prevent leaking any information:
- Lock the phone properly (strong password, fingerprint etc.)
- Encrypt the contents.
- Hide details for notification from the lock screen.
- If possible, prevent answering to any phone calls without authentication. That's probably the hardest step to achieve, and anyone who calls you may accidentally reveal your identity, not to mention if a phone call is chosen for a 2FA method.
- Use a secondary email address that could not be linked to you.
As in Schroeder's excellent answer, the email address is not the most crucial information a phone could leak. The #5 is only truly useful if you have achieved everything in #1-4, as any of #1-4 can make it trivial to find the information hidden in #5.
There is a better solution.. Display instead the phone number of the person you want contacted in case of emergency, labeling it clearly 'ICE' (which means 'in case of emergency' to all emergency workers). Then if you get in an accident and are unconscious your person will be contacted a lot faster. And as a side effect if you lose your phone a friend will get quickly notified too