Does Verizon let you use IMAP? If so, set up your account using IMAP rather than POP and the account in Thunderbird will be synchronised with your webmail, and vice versa. I guess you may have to change some setting on the Verizon website to allow this. Then follow the directions here: https://support.mozilla.org/en-US/kb/switch-pop-imap-account

Thanks so much. However, I discovered that if I opened Thunderbird first, whatever is in the inbox can't be deleted on thunderbird through deleting on Verizon. However, if when I open Verizon email, if a new message is there that I had not yet opened on thunderbird, when I delete it on Verizon, it does delete it on Thunderbird. So, this works for me! Sorry I didn't know this already.