Given how trivial it is to set up serverless Rails using something like ECS Fargate, the benefit of running specifically on Lambda is lower than migrating off a tried and tested technology.
With lambda you pay for what you use. It scales endlessly and is quite cheap. Depending on your typical usage and load it can be a huge cost saver (also mentally) as lambda will scale.
With ECS Fargate it costs money even without any traffic and you are responsible for correctly implementing auto scaling.
I'm coming from 10y rails dev background and now full stack typescript. Thinking in pure lambda functions is a breath of fresh air for me.
if this is powering your primary API and you have 24/7 traffic, fargate can actually be cheaper in some circumstances. there's nuance in lambda config, including concurrency, temp space, and memory. pay for usage is nice until it's not.