Check the net for Alex Viada. He's a strong man power lifter who do ultra marathon too, so I guess he's a good lead.
I my self am not as strong nor conditioned as he, but still doing good. I'm 5'6 feet tall and 167.5 pounds, and I'm a couple of pounds short to 1000 in the 3 big lift total. I run obstacle courses too, from 5 k to more than half marathon in ski slopes and all. I always have both conditionning and strenght in mind as objectives, but a specialize more or less on one or the other depending of the season.
In january and february for exemple that's when I do the less conditionning, cause I'm doing more volume on weight training, doing strenght with hypertrophy second. Conditionning consist of playing ultimate frisbee 2 X a week, walking an 1 h with weight 5 X a week and snowboarding. In march I'll start doing strenght circuit to ramp up the conditionning a bit and hoping for some fat loss effect. half april the same.
then after that it's strenght maintain by doing only 2 lifts a day at morning, adding a tabatha swing or somethin'. mid day is running, most days, differently - full long slow, intervals, short and fast, hill or stair sprints, etc. As summer goes and the races are going to an end, I like working on skills outside (human flag, muscle ups...) then it's autumn, witch is strenght training like 5-3-1 templates 4 X a week and conditionning still 3 X a week on mid day.
SO I DO BOTH, BUT NOT AT THE SAME TIME OF THE DAY.