It helps if you offer a concrete use case, as in how large the heap is, what kinda of blackout period you can handle, and whether the app can handle all of it's open connections being destroyed, etc. The more an app can handle resetting some of it's own state, the easier LM is going to be to implement. If your workload jives with CRIU https://github.com/checkpoint-restore/criu you could do this already.

By what I assume is your definition, there are plenty of "non cloud native" workloads running on clouds that need live migration. Azure and GCP use LM behind the scenes to give the illusion of long uptime hosts. Guest VMs are moved around for host maintenance.

"Azure and GCP use LM behind the scenes"

As does OCI, and (relatively recently) AWS. That's a lot of votes.

Use case: some legacy database VM needs to move because the host needs maintenance, the database storage (as opposed to the database software) is on a iSCSI/NFS/NVMe-oF array somewhere, and clients are just smart enough to transparently handle a brief disconnect/reconnect (which is built-in to essentially every such database connection pool stack today.)

Use case: a web app platform (node/spring/django/rails/whatever) with a bunch of cached client state needs to move because the host needs maintenance. The developers haven't done all the legwork to make the state survive restart, and they'll likely never get time needed to do that. That's essentially the same use case as previous. It's also rampant.

Use case: a long running batch process (training, etc.) needs to move because reasons, and ops can't wait for it to stop, and they can't kill it because time==money. It's doesn't matter that it takes an hour to move because big heap, as long as the previous 100 hours isn't lost.

"as in how large the heap is"

That's an undecidable moving target, so let the user worry about it. Trust them to figure out what is feasible given the capabilities of their hardware and talent. They'll do fine if you provide the mechanism. I've been shuffling live VMs between hosts for 10+ years successfully, and Qemu/KVM has been capable of it for nearly 20, never mind VMware.

"CRIU"

Dormant, and still containers. Also, it's re-solving solved problems once you're running in a VM, but with more steps.