It's doubtful - for the simple reason: a lab-on-chip requires a silicon chip to make sense of the readouts, so increase in production of labs-on-chip will automatically create increase of demand (and production) of silicon chips.
There is an avenue which can overcome that trend - single-use, disposable labs-on-chip, say, preloaded with a dose of a marker substance, so you need to replace it after the measurement, attaching a new one to the same "front-end" silicone chip - say, medical samplers where the readout of given marker of given patient uses up one disposable lab-on-chip, which is inserted into a reader to give the readout. Still, for any reusable lab-on-chip, a silicon part will remain a necessity.
Still again, the technologies may blend - say, you could claim the production of thermal sensor devices outpaced the production of microcontrollers, simply because about every microcontroller on the market contains one or more thermal sensor built in, next to all the production of standalone sensors (which hasn't been outpaced). I can imagine in the future many generic chips including some lab-on-chip components, so along with regular production this may increase the number.