This seems like a fun adventure. I'll say upfront that I've never tried what I'm about to suggest.
When I read your question title the first thing that came to mind is a Puerto Rican sandwich that is very popular in Chicago, the jibarito. It's a sandwich in which the bread has been replaced by flattened and fried plantains. I think doing something similar could yield nice results for a pie crust. You just press the peeled plantains between two cutting boards to get your desired thickness.
As far as not frying, you should also be aware that fried plantains are damn good. I've never eaten a plantain that wasn't fried. That said, if you are committed to not frying I have suggestions as well.
First, the boiling and mashing is right out. I don't think the processing you'll be doing will result in a crust that holds up at all.
Roasting, or better yet, pan frying in butter I think is the way to go. I suggest just greasing a large frying pan with butter and pan-frying the plantain over medium-low heat until done.
If pan-frying is not your thing either, I'd suggest just brushing them with melted butter and tossing in a 400 F (200 C) oven for 10-15 minutes (complete SWAG - never oven roasted plantain). With either the roasting or pan-frying method you may wish to sprinkle each buttered side with a little sugar to add a little sweetness and a nice carmelization.
First of all, lye is not "water boiled with ash". You might be thinking of potash, which used to be used as lye, but virtually all food-grade lye today is sodium hydroxide.
In terms of its function, it largely raises the alkalinity (pH). Baking soda does too, but sodium hydroxide is far more potent - let's just say you don't want to get any on your hands by accident.
The reason some recipes use lye is that alkalinity is a major promoter of the Maillard reaction, which is responsible for the crisping and browning you see in many baked goods - most notably pretzels. I haven't seen cookie recipes using it but I imagine that those recipes would produce very crisp and hard cookies - not my cup of tea but maybe that's what you want.
The only ingredient I know of that you can use instead is baking soda, but I wouldn't call that a replacement, more like a substitution. It will work the same way, but in the end you'll have something much softer and less browned.
There is actually another substance that is in between the pH of sodium bicarbonate (baking soda) and sodium hydroxide (lye), and that is sodium carbonate AKA "washing soda". It's listed as a food additive (E500) but it is rather difficult to find in food-grade forms. As its name implies, it's more commonly used as a detergent. However, it would be a better substitute than baking soda due to its higher pH.
One can make food grade sodium carbonate (Na2CO3) from food grade baking soda, sodium bicarbonate (NaHCO3), by baking it an oven spread out on a cookie sheet at 350° F for one hour; baking longer won't hurt. This drives off water and carbon dioxide to form food grade washing soda (sodium carbonate) which increases the pH more than baking soda.
Here's the reaction for the above process:
2NaHCO3 ---> Na2CO3 + CO2 + H2O
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From On Food and Cooking:
And weaker gluten structure is definitely a good thing for pastry doughs!
From the same source:
So eggs help provide a more tender structure, again good for pastry doughs.