Yes, 1hr is tight. I frequently connect there, and if you are connecting from domestic then it's straightforward, just up the escalator into departures after having your BP scanned. But connecting from GVA you will have to re-clear security (5-10 mins) then transit to T5B or T5C, which can take take another 5-10 minutes. LH flights usually start boarding 40 mins before departure, so at a bare minimum you will reach the gate and boarding has already commenced.

Most of my flights are EDI > LHR > BWI/IAD and I always like 1H40M for comfort.