I don't know that it comes standard, but every 8.8 I've put in from a V8 explorer has had the lsd.
What's funny is everyone keeps talking about the 4.10 axle, and I have yet to see one! I'm sure they exist, but I have done probably 8 of these swaps in the last couple years. Most were 3.73 with a lsd, there were a couple with 3.55s, and both were open. I will note I haven't gone looking for one either. All of them I have worked on were going 33s or larger, so they wanted 4.56 or lower anyway.
If I had to guess, I'd say 4.10s come in the off road package, and maybe just the V6 :dunno:. There should be a sticker with the axle code, there's one on my F-150 on the B pillar. I'm sure someone on an explorer forum could tell you for sure, and how to ID it.
Other than #s, you can tell if it's a LSD by the manual method. Hold the pinion stationary, and turn the other side. If is spins the opposite direction, it's open. If it wants to spin the pinion (axles spinning same direction) it's got a lsd.
It's easier with a lsd, but you can get the gear ratio by spinning the axles one time and counting the number of times the pinion rotates. The important thing here is to make sure both shafts spin at the same time, in the same direction. Otherwise the spiders will rotate instead of the carrier/ring gear.
Or you can just take the cover off and look