Just my opinion that the tolerance to oil weight is a more liberal than manufactures entail when they specify one or a few particular oil brands. Iso 68 is a vary common way oil for various machine tools, 20w is close in viscosity at room temperature Iso 68 so I use that for all my machine ways and slow gearboxes. For my harig the manual specifies SUS 150-225, quite a far range so I use iso 32 as it is a common oil from auto suppliers. It also is well suited for high speed gearboxes as the modern southbend requires. The original oil pump to my harig broke down long a go so I use a small submersible water pump, which seams to run just fine in the lighter oil. https://www.bobistheoilguy.com/viscosity-charts/ https://cdn0.grizzly.com/manuals/sb1056f_m.pdf
the lathe liked requires iso 68 for the ways and slow gear boxes, iso 32 for the head stock.
There is one Logan 2500 Series Operator's and Parts manual and one Parts manual in Downloads. The manuals on most make machines have either a drawing and list or a list or all lubrication points on the machine, along with how often to do it and what lubricant to use. The Logan one has some of that information buried in the text, so you will have to read through the paragraphs to find it. Unfortunately, the recommendation for the headstock sump is for either of two specific makes and type numbers, either Keystone 122-7X or Standard Oil Amovis 5X. They don't give viscosity or generic type. Unfortunately, Keystone was bought by Total who pretty soon discontinued most of what Keystone made and I don't know what happened to Standard Oil. However, the conclusion of one Google search result which is in another thread in this same Forum concludes that the lubricant referred to is grease. That is obviously incorrect as the same lubricant is used on the "oiless" bushing in the driven pulley.
All that I can suggest is to pull the top cover and see what's in there in the Well, which I assume means sump.