This holder was designed as part of a larger effort. It is designed to hold the 1/2 fluid oz tube of lubricating oil and 1/3 fluid oz tube of grease included with the Oster Classic 76 (https://www.osterstyle.com/clippers/oster-classic-76-universal-motor-clipper-with-detachable-000-and-1-blades/076076-010-003.html).
The holder includes spaces for three tubes, as it also includes an optional holder for the little brush that also came with the clippers. The holder is shaped similarly to the oil and grease tubes, and is roughly the same dimensions.
I would expect it to fit the replacement 1/2 fluid oz tube of lubricating oil (https://www.osterstyle.com/accessories/oster-blade-lube/076300-106-005.html) (but not the larger 1 1/4 oz oil and grease tubes), but have not tested this.