The original idea was to pump a normal 40 weight oil from a tank to the mains via the glands.
Splash aided the big-ends and some to the bore.
Then the fuel transfer from crankcase to piston picked up oil from the crankcase (sump?) and transferred it to the combustion chamber (plus cooling and helping to lubricate the little and big ends), this should achieve total lubrication.
So, in this instance the system predated Suzuki et all by around 70 years.
The question of oil type is sightly obscure, the original idea was straight standard mineral oil, 2T oils evolved due to premix only applications (not meant for the Scott but for engines like the Villiers), they are also especially formulated for this role.
Should you run premix through the Pilgrim, NO!!!!
Can you use 2T through the Pilgrim, absolutely yes!! But bear in mind the limitations of the poor, old and much maligned Pilgrim, and do not use a low weight (thin) oil.
Mike