I always love a story about a successful strangler pattern migration. I do wonder how they came to Lambda though. I love it for small workloads and highly variable demand services, but something like Treezor you'd think has relatively flat and high demand. The cloud cost for Lambda would be much higher than running the equivalent compute, even with something also highly scalable like ECS.
We use Lambda (via Laravel Vapor; https://vapor.laravel.com/ ) for a big analytics batch processing job every night; it spawns hundreds of thousands of individual jobs that make various API calls, but only for a few minutes. For the rest of the day it's doing very little. I'd imagine a bank has quite a few of these sorts of bursty bash processing needs; ACHes, end-of-day reconciliation, etc.
You can have a single queue gathering workloads and then have Lambda functions grab a bunch of tasks, handle them, grab more etc. until the max runtime is met and they're automatically rebooted.
It's also pretty trivial to add more processing capacity when the queue goes over a specified limit just by allowing for more concurrent Lambdas.
And when there's nothing to process, you've got one idling Lambda doing nothing and costing nothing.