I set up an appointment time with my LA when I want it done ASAP. I email her when I start a project and tell her the week I think I will have it done. For example, the one I am working on now, I told her will be ready after Labor Day. It is slotted in her schedule for Wednesday September 15. Then I get it back in 1-2 weeks, depending on the size of the project. I have never missed a deadline and neither has she. It has been close though.
The other way I do it is that I drop something off that I dont care when she finishes it. She may have it months and just works it into her slower times. No deadline.