Thunderbird is stuck to one device (desktop). Technically you can have Thunderbird across a lot of computers by using IMAP instead of POP3 but that slows down and cancels out a lot of your speed benefits.
Your complaints about Lightning are misplaced. It's an extension, not part of Thunderbird itself.
=== Security Wise ===
If anyone somehow breaks into ANY of my email accounts I still have access to all of my emails, they can't delete any emails, and they can't read any of my emails. With IMAP they can just look through old confirmation emails and see your username, go to that site, try to log in as you, click "I forgot my password", and have it sent through email, log in with the new reset password and change all your credentials to a new username, new password, & new email so you can never log back in. Effectively creating a massive mess for you to clean up. Email is the greatest failure point of your digital existence.
I've reached a point in my digital life when I realize how insecure I feel to have so much information all over the place with ANYONE in the world able to access it all just by knowing a password. With everyone claiming a stake to own my digital property I feel the best way to truly be in control of my own words is to pull my emails out completely and keep them locally. I want to own my words, I want to completely control where they are and on what hard drive they exist. It makes me happy.