Sounds like costs is your concern .. so keep this in mind: IF any of the server-side code of your app needs to talk to the Internet, you MUST also provision a NAT Gateway for Lambda to use to talk to the Internet. On its own, Lambda has NO OUTBOUND INTERNET ACCESS. A NAT Gateway currently costs .045 per hour, on top of data transfer AND processing charges. With Lambda you only pay for the time the function is running, but your NAT Gateway will be running all the time. On top of this, if your traffic is getting to your Lambda function through API Gateway there is that to consider .. since its a small app, I am going to assume you will never hit the limit to incur the API Gateway charges, however, if you have CloudTrail turned on, you will be getting CloudTrail logs for (1) Lambda, (2) NAT Gateway, (3) S3, and (4) API Gateway .. which may potentially set you up for possible CloudTrail charges.
Now compare this with the cheapest Lightsail instance which costs .047 per hour and already has Internet access. Granted the RAM available is really small, but if you are running a small app .. and hopefully its not written in Java, then this should not be an issue. Also, the stack is much smaller and simpler to manage.
So at a baseline difference of .002 cents per hour (comparing the NAT Gateway cost with the Lightsails costs) .. and also taking into account the simplicity of Lightsail, .. Lightsail could be a better choice.
If you are concerned about the fact that Lambda will scale automatically, keep in mind that you can programmatically trigger additional and larger Lightsail instances and essentially accomplish the same sort of scaling paradigm. Note though, that you can't simply shut down a Lightsail instance you are not using, you must delete it before the end of the month to prevent the full monthly charge.
That being said, for an EC2 instance you dont have to delete it to avoid additional charges, you can simply shut it down .. so actually, I would recommend EC2 over Lightsail because you can make things even simpler.