Do you have a complete upper, or do you need to assemble barrel, handguards, etc? I have not done that, but I do believe you would likely need a wrench (possibly an AR-15 multi-tool) to tighten the barrel nut and attach handguards.
Or are you just assembling the LPK in a stripped lower, and installing the buttstock? If you are installing a buttstock, you will need a specialty wrench. I believe the AR-15 multi-tool would work for that too. I just went to a fellow gun nut friend's house and borrowed it for a few minutes.
Fly