A mobile insurance and device company, Asurion, has announced its findings on a study about missing devices and cases in which their owners managed to get them back. The company reported that having a lockscreen showing a contact number resulted in 3 times the chances of recovering such a device. In addition, the use of a cross-platform browser is a good idea in case of phone loss.
https://www.notebookcheck.net/An-insurance-company-publishes-its-report-on-successful-stolen-or-lost-device-recovery-research.413979.0.html
There is a very easy solution to the lock screen. Simply create a secondary email account, and place the email address in a text note on your lock screen. If the device is lost, the person who finds it sees your secondary email address, and writes a message to it. You can use 2 factor authentication by email to your primary account. Do not connect the device to the secondary account. So, if someone is unable to unlock your phone, they won't know your primary email address. If they see your secondary address on the lock screen, even if they somehow gain access to the secondary address, they can't do anything with it, or use it to unlock the phone. If they gain access to the secondary address, they will be able to see your primary email address listed in the 2 factor authentication. Otherwise, you could create a 3rd email address as a man-in-the middle between the primary and secondary email address for 2 factor authentication, if you are worried about someone being able to gain access to your secondary account and being able to see the name of your primary email address.