I added some conditioning work this spring. I was doing an 8/5/2 program that had me squatting and pressing on Mondays and Fridays, and benching and deadlifting on Wednesdays. What I did was hill sprints on Saturday mornings (Friday was a volume squat day) and a mile and a half jog on either Tuesdays or Wednesday after my pulls. I thought running would suck after deadlifting but it didn't really suck worse than it ever does. I also did some biking on Sundays but not consistently.
Honestly the hill sprints did way more for my conditioning than the slower distance running. The only reason I did any slower running was because I was training to do a 5k with my daughter.
Hill sprints on Saturday sucked too, but they're over quick. And they got easier quicker too. I'm 44 for whatever it's worth.