Question About a 1948 Sunbeam Mixmaster Lemon Pie Recipe

I know I’m younger than most people here, but I hoped someone might be able to help with a vintage baking question.

A couple years ago I inherited a Sunbeam Mixmaster from my great grandmother, and I’ve really enjoyed baking with it ever since. I recently found a 1948 Sunbeam Mixmaster cookbook at a garage sale and decided to try the lemon meringue pie recipe yesterday, but the filling stayed very runny — almost like soup.

I’ve successfully made meringue pies before, so I’m wondering whether this recipe expects the filling to thicken mainly:

* on the stovetop/double boiler,
* in the oven,
* or while chilling afterward.

I've seen so many variations of this dish online, so I'm not sure when the official Sunbeam recipe thickens. I’d really like to make the recipe as originally intended before changing ingredients or proportions. Has anyone here used this cookbook or made similar vintage lemon meringue pies?

I also noticed the pastry quantity seemed a little small for my Pyrex 9-inch pie plate, so I’m curious whether pie dishes were slightly shallower at the time.

Any advice would be appreciated!