Madrid has only one store selling pre-owned watches (L'Ermitage) and it is a terrible dealer. Count on watches in this store being priced at 40% above market prices and in only average condition. Otherwise, there are a few stores around Plaza Mayor and Grand Villa but these shops will have only about 8-10 watches and also way overpriced. Sorry to disappoint you.
C/ Ayala 25
28001 Madrid, Spain
On the other hand, there are several excellent new watch stores and Spanish prices tend to be below the average European prices and USA prices. If you are a good negotiator you can get the stores down 15% and then you get the 16% VAT paid back to you when you leave the EU... which makes for excellent net prices.
Both watch stores ("relojerias") that stock Lange are on Calle Serrano which is very close to Plaza Colon -- right down town. The stores are Wempe and Suarez. Calle Serrano is a large street with many luxury shops, not to mention numerous relojerias. You can find practically any brands along this street from Zeno (at El Cortes Inglese) to Ikepod to Chronoswiss to Lange & Sohne.