They couldn’t give up the actual storage keys because they weren’t stored. The courts wanted Lavabit to implement a mechanism to capture the keys during use, which they didn’t do.
Signal is more secure in general due to end-to-end encryption but user experience is bad. I would use Signal when I really have something to fear very seriously, in this case personal security more important than usability.
Telegram is much better made UX-wise. It's a more decent product for average user. It's a Facebook Messenger alternative which is secure enough and doesn't sell your data to anyone.
If you are not security expert or journalist and black helicopters are not chaising you, you don't need Signal, Telegram is much better messenger with great clients on different platforms.
Better to not have to trust the intentions (or ability to resist torture, etc) of Telegram, Pavel Durov, et al. Better to have end-to-end encryption by default, like in Signal.
https://www.techdirt.com/articles/20131002/17443624734/lavab...