I heard the same story - LA rode silk Dugast tires. $200+ each, aged 5 to 7 years. In a fit of extravagance, I bought a pair of cotton Dugies. Don't know that they're any faster, or that they're actually worth the $90 each I paid for them, but lord are they smooth... definitely old school - the latex tubes go flat after about three days. And don't leave them in a car on a hot day, the rubber will start to come loose on the edges. (tire glue fixes it)
Whatever he was doing, it worked. It was very rare for LA to get a flat or have any sort of mechanical trouble. The man defined meticulous.
Many, many moons ago, when I was spending summers wrenching in a bike shop, we visited the cycle distributor, where I saw a box full of track silks. Beautiful tires, with the thin strip of rubber and silver silk casing. Wholesale was $80 each in 1980, when a dollar was worth a lot more than it is today.