Lol not necessarily. I've broken the 2min barrier 3 times over a period of 4 years. At no point could I have benched or deadlifted my bodyweight. I may have been able to squat it, but it would have wrecked me.
The last time I broke it was maybe a month ago, so I'll give you my stats from then. But, I would have been significantly weaker when I did it the first time and second time (both over a year apart).
6'2. 158lb.
Bench max: 135
Deadlift max: (never did it, but repped 95's)
Squat max: no idea, never did more than 95.
As for the training I was doing, I lifted twice a week max, and only the benching was maxing out, everything else was just activation. (The benching was just for fun, probably didnt help me a whole lot.)
The mileage each time was completely different.
The first time I was fresh off of XC training, so probably 50-60mpw w/ no speed. I don't think I did any more than 3-4 workouts at anything faster than mile pace, but I still had a great kick. Most runs were around 7:00-7:30 pace. Honestly, I have no idea how I broke 2 then, most of my races that season were more 2:04-2:07
The second time I was doing about 40mpw with every run pretty hard. Did a Vo2 session on Tuesday and a pure speed (usually 200's or 300's) session on Friday and a 10mile LR. Every run though was cutting down close to 6:00. That sucked. I was tired all season and I think just hit it right one race. Most races were around 2:02-2:04.
The third time was by far my best season.I had a very consistent summer/fall at 60mpw, no injuries, and no big workouts. A few tempos and thresholds but just gearing up for track. Track I did 35-40mpw in the beginning, with K repeats on tuesdays and hills or 300's on Friday. LR was 8. Except for Tuesdays and Fridays, every run was slower than 7:30's with a number of them closer to 8:00. I ran a number of 2:00's and 2:01's. Best season by far.
In none of these seasons was I doing any serious weight lifting. A lot of strides, a lot of core, and a lot of getting plenty of sleep and eating healthy.
Sorry that was a lot, but hopefully it helped. My theory here is that it doesnt really matter what you are doing, so long as you are committed and living the right lifestyle when youre not training.