Unfortunately you cannot use oil lubrication on a vertical installation. Some mechanical applications use bearings of different diameters. This makes it impossible to maintain a correct oil level. Vertical applications have the same problem. Oil mist is the preferred method if you can solve the fugitive emissions problem .
Oil mist can provide a positive pressure inside the bearing to keep out contaminants.
Mixing the oil with air presents a problem because of venting hydrocarbons to the atmosphere. If you find the bearing lubricant is getting too hot, most pumps have a facility for cooling the oil in the bearing case. Never attempt to cool a bearing by cooling the outer case. In other words if you cool the bearing case it will contract or shrink and increase the load on the bearing. Lubricants are made from various oils and additives.