Food grade lye on counter tops
The biggest problem with lye lies (pun intended) in the fact that it is a strong base (lye is a metal hydroxide, usually sodium and/or potassium hydroxides) and will attack some metal surfaces such as aluminium strongly. Generally most other compounds are non-reactive unless they can form some sort of acid-base reaction.
Quartz countertops are engineered stone - that is finely ground stone powder/chips held together with resins, usually polyester or epoxy resins. Polyesters are readily attacked by alkali, while epoxy resins are more resistant (see entries for potassium and sodium hydroxides) so, in absence of knowing which resin has been used to make your countertop, I wouldn't allow lye to sit on your quartz for an extended period. Indeed use of such chemicals is not recommended for quartz countertops at all - partly because it can permeate into the pores in the stone surface and contaminate food later.
Lye will dissolve lignin (the main component of wood) to some extent, but I think this is fairly limited. However, as with the countertops, fake woods are held together, with - you guessed it - resins (different type). In the case of MDF and particle board, these are held together with urea-formaldehyde resins, which seem to be quite resistant to hydroxides (Warning: PDF). You will find that the biggest problem with these sorts of woods is water getting into them and causing the wood component to swell and mechanically break apart the material. However, this problem isn't specific to lyes.
Ceramic tiles should be completely resistant, but the grout between them probably isn't completely resistant as that is usually made up of cement with some epoxy resin as binder. Hydroxides will attack the grout slowly (as noted above for epoxy), but so long as you can clean the lye off fairly quickly, it should be fine.