What actually did happen in the Lavabit/Snowden case?
The government ultimately did not get the access they sought. Instead, their fast-paced legal intimidation tactics achieved nothing but to induce Lavabit's owner to shut down the service. If the government learned anything more than Snowden's actual Lavabit email address, they likely did it by compromising machines outside of Lavabit's control.
Now, what actually would have happened had Snowden been able to use ProtonMail?
The U.S. government would have been unable to issue fast-paced, overwhelming and compulsory orders. They'd have to go through the Swiss court system. They would not be able or allowed to cloak the proceedings in secrecy. Even assuming they were successful, they likely would not be able to get the kind of sweeping direct access they were demanding from Lavabit; if they were awarded anything, they would likely be awarded info about specific accounts. And ProtonMail would in any case continue to function.