Factory LSD swap for base model?

Alright so I have the 2wd base model from 2010 and it has an open diffential with the shitty auto LSD system. I've read that apparently some trucks came with an LSD from the factory so would that be something I could swap in? Or are there any aftermarket LSDs that would be a direct replacement? For the record I'm looking for something less off-road oriented and more street/drifting oriented, since the goal here is to get sendy on the backroads and dirt trails in my lowered truck. Figured I better make a post before I change the oil in my stock diffential for my 30k service. Thanks for any help or ideas tw friends.

 

A detroit truetrac is what I recommend

 

It’s a helical style LSD so it’s an upgrade over the factory one that had clutch packs

 

What size would I need to look up for the 4cyl 2wd? Most seem to be for 4x4s

 

You can call east coast gear supply to be sure, but I’ve heard of ppl swapping in 3.73s in the 5 lug trucks, so I’m betting the truetrac for the 4wd/Prerunner trucks is what you need