On my rooted Android it detected that I had root and prevented me from using the app. Lloyds Bank mobile banking doesn't have any similar scruples.
However, my assumption is that it's a security measure. They are presumably trying to stop malicious applications sending payments without user notification, and I guess that makes sense.
As a bank, they may be being overly precautious, but is there a fallback of a web app?
If you were a casual root user, installed this app, and there was some back-door only accessible via rooted phones, it would be the bank's problem.
Whether this is a reasonable security measure or not, I imagine it was their line of thinking.
Casual root users are at enormous risk of malware, like running XP without a firewall levels of risk.
When I give all my money to someone for safekeeping, I would much prefer they err on the side of caution.