DRO stand for Deep Resonant Orbit. I've been playing with these on Jenkins' orbital simulator. The are more stable than prograde orbits and can have apolunes up to about 40,000 km (if my sims are an indication).
Here's some screen captures:
From these I concluded DROs having an apolune can be very long lived.
Here's a screen capture of some orbits I let run a little more than 100 years:
The sim includes earth's as well as the sun's influence. These orbits will stick around for a long time.
At first I thought DRO to EML2 was .4 km/s. EML2 is slightly prograde and thus something from a retrograde orbit would need to kill all it's velocity and then some at apolune.
But stumbling on LEO to EML2 via ballistic capture made me wonder if something similar is doable for DRO to EML2.
For a ~.2 km/s burn from a 40,000 km DRO I've been able to get a 450,000 km perigee moving at ~1.2 km/s. But this perigee also needs to be close to the moon, something I haven't been able to manage yet. This is the closest attempt:
From a DRO maybe there is a ballistic slide into EML2 but I haven't found it yet. But the above orbit could be tweaked by small burns at apogee. It's moving very slowly at apogee so I believe a high ISP, low thrust ion engine would be up to the task.
It doesn't take much to park an asteroid with C3 just above 0 in an LDRO. With existing rockets like the Atlas V we would launch asteroid retrieval vehicles capable of parking 100s of tonnes of asteroids in stable lunar orbits.