This kind of workload could easily be handled by a pair of t2.micro instances. This would cut your costs for dedicated servers to around $0.40 a day.
Plus, you could then take advantage of persistent in-process memory caches and warm services, helping to speed up your responses even further.
Using tools like Lambda come with a number of advantages, but you give up a lot of control at the same time. Perhaps this isn't a problem for most side projects, but for business critical software I'd be very leery of handing that much control over to someone as uncommunicative as Amazon.