Ahh, the elusive quest for a Lestercaster. For starters, scale length and construction will play a huge part in it.
You're probably going to have to choose whether you are going more for a Les Paul humbucker, or a spanky Strat. In my experience, a set-necked, mahogany bodied guitar with 'buckers and coil splits will get you far closer to the Gibson end than Fender. And a 25.5" scale superstrat never quite gets thick enough to cop a true Gibson tone.
I've tried the Swiss Army knife thing a number of times. My first try was a Hohner Steinberger copy years ago. Then a PRS Cu24 which is a rippin' superstrat, but never quite gets to Gibson or Fender territory.
The closest I have gotten are with two guitars - first is the PRS Studio (the more recent version). This has 3 humbuckers - bridge is the 57/08, which may be the sweetest, most open sounding vintage-type humbucker I've ever heard. However, the 57/08 starts to fall apart under higher gain - I really don't care for it much past AC/DC territory. The other pickups are the Narrowfields. These are great pickups, but aren't quite fish nor fowl. With the volume rolled back, they get close to a hybrid of P-90 and Strat pickups, but they're not going to convince you you're holding a Pre-CBS Fender. The pickups balance very well unless you've split the bridge. The middle Narrowfield is a bit intrusive if that's where you pick. Build quality is outstanding, the trem is simply amazing, and it's gorgeous.
The second one I have is my most recent - a custom-order Suhr Classic. Mine is an alder body, roasted maple neck and Pau Ferro fretboard. I got the DSV bridge humbucker and two V60LP singles in neck and middle. I have the bridge pickup set to switch to parallel rather than split, which is a tone I really like. These pickups balance extremely well. All positions are useful, but there is zero quack in position #2. Position #4 is one ducky-sounding MFer. The bridge humbucker is very low output in order to balance with the singles in neck and middle. It's open and very wide-sounding. I tend to have to increase the gain levels with this guitar to match my other humbuckers. That said, this guitar is the one I'd grab if I've got to do a variety gig with one instrument. I can get close to about any tone I'm likely to need. The neck single coil is amazingly sweet and bell-like. The middle position works well, and the bridge pickup can chug well if you've got enough gain. I got the SSC system so it's dead silent in all positions. And the trem is very stable and feels great.
Suhr makes some amazing guitars. The reason I went custom was that I wanted a 1 11/16" nut width, which is not available on the Pros. So I went all-in and had one made the way I'd want it. If you can deal with a slightly narrower nut, look at the Pro models. If you want more of a neck humbucker tone, look into the Moderns. The Modern Pros look better, but I've found the Modern Satins to feel and sound better.