I have one similar that looks like No 68.
I see no mention of the 68 or 88 in the Rayo catalogs.
The D-Lite size globe that fits it is called a No 100 C B globe for lanterns 99, 100, & 102 in the latest catalog I have.
The 99 is a Firemans lantern, the 100 is a barn lantern very similar to yours, but with a flat top fount and 10.2 Candle Power. All of the Rayo's that I have seen with the No 100 globe were made by Prisco, you can tell by the unique lifter.
Your lantern may be from the 30's that I do not have a catalog for.
Rayo also had other manufacturers make lanterns with Rayo markings.
John M