Hi,
When you say "lawn mower" are you referring to using a transmission / transaxle from a ride on mower?
If you run a large drive pulley and small driven pulley the gearing will be too high. ( rather than taking off, the engine will probably stall) These use a tensioner style clutch.
In standard form the drive pulley is smaller than the driven pulley. I have read in mower racing applications the pulley sizing is altered eg: 1 : 1. ( bear in mind the transmissions are also modified to handle the additional load and speed)
Also, I'm not sure how you will go finding a pulley to attach with the centrifugal clutch. Most use a chain drive or as the reply above suggested, a TC.
Hope this helps,
Cheers
Toystory sent his reply as I was typing mine....