The Lucky prefix has, as the first part of its benefits, 'Critical shots do double damage'. Since 'normal' crits already do double damage, I'm assuming adding the Lucky prefix actually means that now your crits will do *quadruple* damage? Second question, can I assume the Lucky prefix applies to all crits with that weapon, including automatic sneak attack criticals when you aren't in VATS?

Not hard to test in Fallout 4 due to criticals not being random. Get a normal version and a Lucky version and fire both at a turret. The normal version will give you your baseline while the Lucky version will show if it is quadruple or triple the damage.

Sneak Attack Criticals do a specific multiple for their damage depending on your perks. If you get a higher damage from the Lucky version, then it does affect other criticals.

Since sneak attacks are separate from the crit mechanic its as I understand its not affected by crit increasing effects like so.