Lancs have been very good with me recently. Turned around a variation within 3 weeks - not super quick, but not too shabby either.
I emailed them first asking about the time they'd take for the variation, as I wanted to hold onto my ticket, as I was off on a trip. In the end I sent in the forms and a copy of my FAC to get the ball rolling, followed by the original FAC on my return from the trip.
Are you in Euxton in Chorley? Your FEO could possibly be another matter, now that George Stokes has retired. I've only dealt with George but I understand his successor can be a little less reasonable, on occasion.
To be honest it is all a big game really and its about knowing how to play it and what to put on the forms etc! I've tended to find Lancs were reasonable with me if I was reasonable with them. They did refuse the 50cal for long range rabbits though....
Cheers,
hh