As far as we know already, when you run a lambda function it is already running in a container - that is how it is engineered at AWS (not sure if they have officially documented that), so my guess would be no, you can't pull a docker container into a lambda function.
However, if what you want to do is run docker containers in a more/less serverless way, check out aws fargate:
AWS Fargate is a technology for Amazon ECS and EKS* that allows you to
run containers without having to manage servers or clusters. With AWS
Fargate, you no longer have to provision, configure, and scale
clusters of virtual machines to run containers. This removes the need
to choose server types, decide when to scale your clusters, or
optimize cluster packing. AWS Fargate removes the need for you to
interact with or think about servers or clusters. Fargate lets you
focus on designing and building your applications instead of managing
the infrastructure that runs them.
https://aws.amazon.com/fargate/