If you manage to lazy load your routes it may help with cold starts but I think you effectively lose the benefit of warm handlers since every request could use new code that needs to be loaded fresh.

I've never attempted lazy loading inside a Faas platform but I think generally you would be better off creating small deployable chunks and letting the platform handle scaling them up / reusing as necessary. Less fighting against the platform and if you have to maintain strict boundaries to enable lazy loading only the needed code for each route it's a short step to deploying those as their own functions anyway.