It sounds very much like Lola already is comfortable with you if she is being vocal.
Do you still offer her the treats? This is what i would start with, see if she will accept them first of all while she is in the cage then you could progress to offering when she is out on the playstand.
I think its really important to try and not be nervous before you begin any contact really, greys will quite easily pick up on this and you are more likely to get a bite if you show you are nervous at all.
Take small steps and build up her trust, eventually you can try to pet and work with step up while she is on her playstand, you say she has not tried to bite before so hopefully she wont try to bite you as she is used to you already.
Good luck and keep us up to date with any progress you make, I hope all goes well and you can have more physical contact with her:)