I bought the L & S from John way back and finished reconditioning it. The times I ran the lathe, I did recall a little bit of seepage from the headstock bearing cover. I've seen this type of leakage before on older lathes in my past.
The first thing I would do is replace the sight glass on the front of the head stock. Real easy to do, bust the glass out, drill and tap a 1/4-20 or 28 hole thru the back. Take a large socket and bolt and washer and pull it out. That sight glass is a standard Bijur part that the last time I looked, it is still available. Replace it, while you are at it, pull the Cuno filter and clean it. Last drain the head stock oil sump as John is talking about and might not hurt to flush out with some mineral spirits or diesel. Then fill with a ISO 32 or 46 hydraulic oil. This oil should have additives that my help unclog some of the oil passages that may reduce some of the oil leakage that you are seeing. I wouldn't try to pull the spindle to clean out those passages. That's not an easy spindle to pull and put back end IMO. Ken