I started off using Lambda as well and made the same sort of mistake. I can't remember exactly how much my bill was, but it was enough that it would have drained all my savings and effectively kill my startup. AWS was kind enough to write off most of it.

We now use Lambda only for simple cron / background tasks, or consuming from Kinesis. We use ECS for everything else. ECS is nice because it's relatively simple compared to K8, but still gives the full benefit of running multiple containers on one box.

I wrote a blog post last year about our migration over to ECS and experimenting with various ways to cut costs: https://blog.bigpicture.io/how-we-cut-our-aws-bill-by-70/