How do I migrate a VM from VMWare ESXi to Lightsail?

You are correct that you cannot use AWS Application Migration Service (MGN) with Lightsail.....it only supports EC2. With Lightsail you have to select one of the images listed here. Ubuntu 20 is an option but you would need to manually configure Gitlab or use a launch script, you obviously would also need to restore your existing data...

If you chose to use EC2 you could migrate your onprem VM using MGN or use a preconfigured Gitlab AMI and restore your data (this would be what I would do). The costs should be just as easy to estimate once you know the instance type you need.

If you choose to migrate to EC2, there is also the option to use AWS Backup, where it will backup your VM and restore as EC2.

Its that way because Lightsail instances aren't freely configurable the way EC2 instances are. See this Knowledge Center article for a breakdown on the differences.

MGN, AWS Backup, VM Import/Export all work in the same basic way - they convert a VMware VM that is backed by a VMDK file to an AMI image that can be booted as an EC2 instance. You can't provide your own custom AMI with Lightsail, you have to run one of the prebuilt bundles. Constraints like that are one of the ways AWS is able to offer lower pricing for Lightsail vs. EC2 instances.

You should also consider taking this opportunity to deploy Gitlab as a container instead of a full server. That will make future portability simpler.