"Hello! Have I got an opportunity for you! I managed to get my hands on that Atlas armory for a song. I guess I have you to thank for that, eh? I've fixed it up good as new and you wouldn't believe how much I was able to salvage. I am in a giving mood right now and would be willing to give you a 'shopping spree' if you do some work for me. Here's the deal. If you could eliminate some of the remaining Crimson Lance then I could be sure they won't try to take it back from me."
Go to a Lance-infested area (such as the roadblocks) and begin killing them until the mission is complete.
Badass Lance (including Ajax) will only count as Badass; Badass Shock Troopers do not count for Shock Lance, etc. Given the relative scarcity of Badass compared to the base types, this will probably not be an issue.
"That many, huh? Not bad. Not bad. I think that is worth a crack at my new warehouse."
This mission is the only way to get a second shot at the chests after Loot Larceny. The glitch linked in that article can still be exploited, however.
If the two roadblock areas in the Ridgeway are cleared twice each, and then clear the roadblock area in the Crimson Highway once, enough Lance will have been killed to complete the mission. Note that some Badass spawns are random.