I had to express Poppet's anal glands all of the time. I do Boo's every once in a while. It's really easy, though it's a very smell and nasty job. Once, I had my aunt hold Poppet while I expressed and it squirted in her hair. Ack! It took two showers to get the smell out. I know I shouldn't have laughed but...
One word of advice: use a baby wipe when you do it. My vet use to use paper towels soaked in some kind of pungent oil to keep the smell down, but baby wipes pretty much do the same thing and can be used to clean the area when you're done. Don't just use some tissue. Gland funk WILL soak through and the smell is just nauseating.
Here's what you do. You get situated near her backside. I usually put my arm over Poppet to cradle him under my arm and grabbed his tail with my left hand. For the first few times, you might want to have help or do this on a table where she won't jump away. Raise the tail up and back...that gets the glands to sort of "pop" out. Grab the wipe with your hand but leave it on only one layer so you can still feel the glands. They're like two little pebbles or marbles on either side of the anus. Imagine the anus as a giant zit...place your hands to the outer side of each gland...push in slightly to get "under" the glands...then squeeze and pull up in a squeezing motion until it expresses itself. Make sure the wipe in your hand is fully covering your hand and hovering over the anus opening so that if it erupts, it doesn't get in your hair or face like my poor Aunt Alice.
Do this once or twice...no more or it might irritate it. Wipe gently with the wipe. Toss wipe into very bottom of trashbin so the smell doesn't permeate kitchen.
Having the vet or groomer do this is fine if it's an occasional thing, but if your Lily is anything like my Poppet, this might become a regular enough event that it be prudent you learn how to DIY.