Can you use parchment paper to lift pies?

Disposable Aluminum pie pans get my vote! They're cheap and work great.

Thrift stores are also a great place to inexpensively stock up on items like pie pans, but the mismatched sizes you may encounter can mess with your production consistency and timing.

While theoretically possible to lift a pie from a pan with parchment, I recommend you seek more pans instead. Could you purchase foil pie pans to use and give away? If you want to avoid contact with the aluminum you could still line the pans with parchment. My local Dollar Tree sells pretty sweet steel pie pans that don't break the bank when you stock up on them. Decorative heavyweight paper pans (with and without lids) are also made for exactly this purpose. Among other stores, King Arthur Flour carries them--search products for "paper pans." I think the Food52 store even sells them, but the search engine is so obtuse that it doesn't spit them out when searching for "paper pans."

Also, of course, if you are pre-baking the crust it can be removed easily and filled afterwards. With some pies, it might be possible to invert the pie over a plate and remove it that way, but it would need to be a very stable type of filling.

Once stationed outside the US, where foil pie plates were unavailable- I rigged up my own using heavy duty foil and cheap paper plates. I had two pie plates of the same size, which I used to mold them. I cut a paper plate to fit the bottom, sandwiched it between two top and two bottom layers of heavy foil, and pressed the foil sandwich between the two plates to create my own. It served the purpose, but I can't say I would recommend it if you could simply purchase cheap foil pie plates. It was a more expensive solution, for one thing, and labor intensive. I don't recall my homemade versions changing the baking times much, but the bottoms did not get as brown due to the extra layer of the paper plate. Never had a compelling reason to repeat the experiment, so I can't say if the success was due to luck or if it would work reliably each time. I used mine to make pumpkin, pecan, and mincemeat pies- which are not particularly wet when done, and tend to hold shape on their own. Not sure it would do for a fruit pie.

Foil is a better choice for lining a pie plate, but picking either up by the edges will place a lot of stress on the pie, tending to fold it in half. Using tart pans where you can lift the bottom disc out is a possibility, but of course they're shaped differently than they typical American pie. I have seen metal pie plates with this feature, but you'd have to hunt them out at yard sales or something. My experience is that a pie will hold up on it's own (haven't tried it a ton of times), but of course it depends on your crust. I once dropped a cherry pie taking it out and it somehow managed to slip out of the pan and land intact on the open oven door- couldn't do it again in a million years.

Another thought: if you are making the pies as gifts, what about an alternate to pie, such as quick bread (banana bread, cranberry orange bread, etc.) that you can make in foil loaf pans from the supermarket or dollar store? The breads last longer, easier to freeze, easier to wrap.

Sure, you can certainly lift a pie out of dish on parchment (imho, you need a second pair of hands). But after that, it will collapse left on its own - it needs to be in a "container." Just bake the pies in inexpensive foil pie pans from your supermarket. They work just fine.