Limpy can succeed if he rolls a natural 20, or if Dexter rolls a natural 1.
1) The initiative rules are different from the attack rules so that your stat adjustment always matters. It wouldn't make sense if Limpy rolled a Nat20- an autosuccess- forcing Dexter to roll a Nat20 himself. That way, he actually beats out Dex's rolls between 12-19, and Dex's autofailure with a 1 gives Limpy more chances to succeed on the low end as well.
I object to Limpy succeeding if he rolls a natural 16 and Dexter rolls a natural 7.
Why? It reflects Limpy doing the best he possibly could while Dexter gets distracted.
It happens.
I ruled my HS chess club.* It wasn't even close. But one day, I was scheduled to be playing a bottom ranked player, I was more interested in reading a book. In my arrogance, I continued to read while playing. Thus distracted, I lost to Fool's Mate- my first and only loss. (Yes, I was ridiculed for it...good naturedly by most.)
On the flip side, I also used to play volleyball a lot. Some of the guys I played with were Olympic hopefuls, and they taught me a lot. So one day, I went out to a beach volleyball bar/club and was asked by a couple to be their third for a game of pickup 3 on 3. They were practicing for some regional event. For whatever reason, it was as if I were a man possessed: every set I made was perfectly placed for his spikes; every pass I made was on target; my serve was dropping in for aces; I dug out or blocked vicious shots from the opposition. It looked like we had been playing together for months, and we blew them away. Likewise the next 3 teams that took the court to challenge us. At the end of the evening, the guy & gal asked me to join their team permanently. Flattered, I confessed that I had never played that well in my life, and they were better off finding someone who could do that on a regular basis. (For the record, while I still played well after that, I NEVER played THAT well again. Not even close.)
* to put my dominance in context, 3/4 of my graduating class were National Merit scholars, and no class at that school since then has achieved less than 50%.