Glorious Enforcer's triggered ability checks whether you have more life than an opponent at the beginning of each combat to see if it triggers. If you don't, the ability won't trigger at all. The ability will check again as it tries to resolve. If you don't at that time, the ability won't do anything. You must have more life than an opponent at both times for Glorious Enforcer to get double strike. It does not, however, need to be the same opponent both times.

After the triggered ability resolves, Glorious Enforcer will continue to have double strike until the end of the turn no matter what players' life totals are.