They should NOT have Loktite on the splines.
Oil would be fine as they slip together and are constantly bathed in
oil during operation. The NEW NEW NEW pinion nut (do not reuse the original) is a mechanically locked torque retaining nut. It does NOT need Locktite. The mechanical thread interferance and the required torque for the nut keep it tight. If at all possible use a machined spacer in lieu of a collapsable one.