Does AWS Lambda run every invocation in a separate Firecracker VM?

I am aware of the cold-start and warm-start in AWS Lambda.

However, I am not sure during the warm-start if the Lambda architecture reuses the Firecracker VM in the backend? Or does it do the invocation in a fresh new VM?

Is there a way to enforce VM level isolation for every invocation through some other AWS solution?

Based on what stated on the documentation for Lambda execution context, Lambda tries to reuse the execution context between subsequent executions, this is what leads to cold-start (when the context is spun up) and warm-start (when an existing context is reused).

You typically see this latency when a Lambda function is invoked for the first time or after it has been updated because AWS Lambda tries to reuse the execution context for subsequent invocations of the Lambda function.

This is corroborated by another statement in the documentation for the Lambda Runtime Environment where it's stated that:

When a Lambda function is invoked, the data plane allocates an execution environment to that function, or chooses an existing execution environment that has already been set up for that function, then runs the function code in that environment.

A later passage of the same page gives a bit more info on how environments/resources are shared among functions and executions in the same AWS Account:

Execution environments run on hardware virtualized virtual machines (microVMs). A microVM is dedicated to an AWS account, but can be reused by execution environments across functions within an account. [...] Execution environments are never shared across functions, and microVMs are never shared across AWS accounts.

Additionally, there's also another doc page that gives some more details on isolation among environments but again, no mention to the ability to enforce 1 execution per environment.

As far as I know there's no way to make it so that a new execution will use a new environment rather than an existing one. AWS doesn't provide much insight in this but the wording around the topic seems to suggest that most people actually try to do the opposite of what you're looking for:

When you write your Lambda function code, do not assume that AWS Lambda automatically reuses the execution context for subsequent function invocations. Other factors may dictate a need for AWS Lambda to create a new execution context, which can lead to unexpected results, such as database connection failures.

I would say that if your concern is isolation from other customers/accounts, AWS guarantees isolation by means of virtualisation that although not being at the physical level, depending on their SLAs and your SLAs/requirements might be enough. If instead you're thinking on doing some kind of multi-tenant infrastructure that requires Lambda executions to be isolated from one another then this component might not be what you're looking for.