I don't know if this will answer your questions, but standard lugs do come in different angles, and the frame designer choses the appropriate lug angles closest to the angles needed. Lugs can be tweaked a degree or two (or even more if the lugs don't have a lot of meat).

Henry James investment cast lugs can be ordered in 1 or 2 degree increments and can be altered a degree or two either way. Each lug can be ordered separately to make up a set of three with any desired angles. Seat lugs are available in 73, 74, and 76 degree angles. The lower head lug comes in 57, 59, 60, and 62 degree angles (this is the angle between the head tube and the down tube). The upper head lug comes in 72, 73, and 74 degree angles.

Looking at your hypothetical 56 x 56 frame with 73° HTA and STA, and the down tube angle is 47.1° (all angles are relative to a baseline drawn through the centers of the front and rear dropouts). That makes the angle between the head tube and the down tube 59.9°, so your three lug set would consist of a 73° seat lug, a 73° upper head lug, and a 60° lower head lug (you'll have to tweak the lower head lug 0.1°).



Looking at your hypothetical 62 x 62 frame with 73° HTA and STA, and the down tube angle is 43.2° (all angles are relative to a baseline drawn through the centers of the front and rear dropouts). That makes the angle between the head tube and the down tube 63.8°, so your three lug set would consist of a 73° seat lug, a 73° upper head lug, and a 62° lower head lug (you'll have to tweak this one 1.8°).



For consistency, the BB drop in both cases is 70mm.