I’d advise against using Meteor in lambda - Meteor’s startup time is fairly long, and lambda by design has short running requests, where you are charged per 100ms of compute time, including that spinup time. It’s also worth noting that your API will be delayed until Meteor has started, and multiple parallel requests will never be sent to the same lambda “server” (though subsequent requests might be).
That being said - there is nothing to stop you writing your Meteor method as a lambda function, or a generic piece of code that could be called from a Meteor server or Lambda. In general I’d advise you setup lambda@edge using cloudfront, as this is the easiest (and cheapest) method of invoking lambda functions directly (you access it from the cloudfront distribution URL). With the added benefit of being able to cache the results if you want.
However, connecting lambda@edge with a DB can be tricky, as the lambda function will run in multiple data regions. If you find the setup too arduous, you can run lambda “as is” (e.g., not at edge) but you’ll need to configure the API gateway, which has it’s own cost associated with it.
Are you hoping to use lambda for more than just “method calls”? e.g., HCP?