Bounty hunting can help to clear a Lockdown, but depending on the situation of a Minor faction (MF) in their various Systems you have other choices as well.
If your MF doesn't control all assets in your System(s) then you can use the Outposts / Stations / ground Ports of other NPC MF to still have access to your Missions / Passenger Missions etc. This is quite vital to alter the % from within a System.
Assuming you have that choice, there are two other ways to break a Lockdown:
1. Expansion
Push your MF over 75% to trigger an Expansion. This state (along with Retreat and Investment) is considered mid-tier in means of importance and thus disables all low-tier states (Boom, Bust, Civil Unrest, Lockdown, Famine, Outbreak). Your Lockdown should be over in 5 days.
2. Conflict
Equalise your MF with another NPC one to make a conflict go pending. If possible (and assuming your type of government allows it) go for Elections. But when desperate a War / Civil War will do too, though during that time people can continue to kill your Security / Civil crafts to have another Lockdown / Civil Unrest go pending. During a Election that isn't possible.
If the rumors are true then we'll get a beefed up NPC Security with the next major update, capable of taking out heavily engineered player ships or at least giving them a much harder time to commit their crimes. Let's hope for the best.