Isn't lambda suicide for a startup? Think of all the lock-in here. If you go big you could suddenly find yourself really stuck if you're overly dependent on it and the overhead of lambda/gateway is too much.
Google App Engine and Heroku and Azure also have lock-in too, to varying degrees -- but at the start it still makes sense to use these sorts of services rather than worry about lock-in. (And if someone later gives you $100k of compute credits on their platform, and it costs you less than that to rewrite the "lock-in" parts, then you still win.)
With no upfront costs and w/o the need to manage servers I'd say it's actually the other way around! ;)