First thing first, if you are aiming for Jerry's tone IMHO anything vintage-voiced pup will get you pretty much there, Fender good quality ones or boutique make no difference.
If you want to get into the nitty-gritty however A5 60s style pickups are "not going to take you there".
The two kinds of 60s pups, early and late "grey bottom", sound much more HD and aggressive than A3 50s pups. The 50s voiced pickups will get you closer to Jerry's tone, which, in the grand continuum of Stratocaster typical soundscape, is a bit rounder and lo-fi (probably he was cool with it coming from years of humbuckers or hollow guitars).
I had experimented a bit with pickups in the last months and tried different combinations of 60s and 50s voiced pups. To my ears, the "muffled" strat sound of Veneta's Birdsong was impossible to achieve with A5 pups. We still have to keep in mind that tapes and consequential mixing made the sound warmer but still you can hear a roundness on the edge of breakup that A5s don't have, as the 60s have more clarity.
John Mayer lately with D&C is using his Silver Sky, which early 60s voices pups. He's a good reference point on how they sound compared to 50s alnico pups.
About products, I can't stress enough to check Radioshop Pickups https://www.radioshoppickups.com/
They are two Welsh teachers that have a small shop and are getting slowly bigger and bigger in Europe. They found out a way to make pickups more dynamics by tinkering with potting during the production of every pickup, done by them by hands; they are called ID on their website but you can ask for custom builds and ID everything you see or wish from them.
They are providing pickups for young acts like Chris Buck (who is a fantastic player). Since they are quite small still, they offer pickups at good prices compared to other boutique makers but they are on par with the best out there and give you even more with this new "technology".
ID pups cannot be described easily but they are one of the best things I've ever played especially if part of your playing is meddling with dynamics.
It's like every pickup has a set of fixated volumes and tones you can achieve by the way you pick the strings. For example volume 1-2-3-4-5-6-7-8-9-10. With IDs it feels like you are capable, if you wish, to get tones infinitely more complex, like having the possibility to play 1.1 - 1.2 - 1.3 - 1.4 - 1.5 - (...) 2 - 2.1 - 2.2 (...) . 3 - 3.1 and so on. This is especially evident If you use your fingers while playing.
On my strat I have their ID:57 in Middle and Bridge positions (with a 60s pickup from them on the neck) and I don't see how and why I would swap them for the rest of my life.
Fender also sells Pure Vintage 59 pickups which are stellar but under-rated because well they are not boutique and guitar players are cork-sniffers. They were part of one of their best lines of guitars ever and voiced and produced with extreme attention to detail.
TL;DR Yes, Lollars are fantastic but Radioshops are better