Try making bigger circles, your horse may not feel comfortable picking up a lope in a small circle.
You could also try lunging her over a jump, horses are naturally inclined to land in a canter after jumping something.(also helpful in getting them to switch leads)
Whipping and whipping is never a good idea, instead of doing whatever it takes to "force" your horse into doing what you want, look for ideas that will make her want to go into a canter.
If you have access to a round pen you could try asking for a canter in there without the line on her which will give her more freedom of movement.
Is it that the horse doesnt want to lope, or doesnt know thats she's being asked?
She could be hurting too, make sure you check her over for any signs that not wanting to lope arent because of an injury or bad feet.
Good luck! :)