Faction restarts are based on the generic restart of their house, which is what causes the rep inaccuracies for foreign allies, and in case of LWB rep on various restarts, it's because of the -0.55 rephack to LWB on Freelancer ID (equipped on house restarts). It's been mentioned on multiple occasions though, that restarts are not meant to give you perfect rep and are only there to increase the time efficiency of setting up process to a reasonable extent.

That said, I've already cleaned up some restart reps for the next update (LWB allies included), but they're still far from perfect and it's unlikely that they'll ever be, unless I again find myself in the middle of an awfully boring evening with absolutely nothing to do. If you have a specific set of reps in mind, you'll have to sacrifice some time by using a different restart which has a rep set closer to what you have in mind (or no restart at all. remember the good old days?) and then flying to your faction base and getting the ID yourself.

P.S: Of course, if anyone's willing to clean up the rep sheets of all the 87 restart templates we have running on GC (each with reps to 101 factions listed. That's 8787 reps to go through and adjust based on faction diplomacy) and send em my way for implementation, I wouldn't mind tossing them in, but far as my own dev to-do list goes, fixing the restart rep inaccuracies is way down the priority list.