I see the manual mentions a 20 hour run time

Can it be charged/ continuously powered while in use ?

Currently in the middle of a 3 month sequence of some seed heads opening using a Hahnel Giga T timer that I have opened and wired jumper leads to battery, and external PSU

Can the LRTimer be run in a similar way for extended periods with external power ?

Yes of course. Just connect am USB power adapter/charger and the LRT PRO Timer will run from wall power.