I suspect that the staining is due to a chemical reaction between the lead and the glass.
Rain water can be acidic due to dissolving carbon dioxide from the atmosphere. This makes carbonic acid. I suppose that this could dissolve a minute amount of lead to form lead carbonate. This could react with the glass over many years and in bright sunlight.
If I'm right, it's incorporated into the glass surface and won't come off.
I stress that this is only an idea and I have no evidence for the truth of it. It might well be utter rubbish!
I have a similar lead stain problem on one customer's window, and nothing will shift it. I've even tried a scraper - and that won't touch it. The only thing left to try is jeweller's rouge, and I'm not going down THAT route.