It is in the ecosystem in the sense that it ultimate boots up an EC2 instance. It is essentially a simplified skin on top of EC2 where AWS makes most of the decisions for you in regards to server setup, with simplified pricing. And it shows up as AWS on your bill, and can be billed along side other AWS services you use.
However, it isn't really in the ecosystem as I would argue. You can't connect it to networks and subnets you create. You don't have control over availability zones, so essentially everything (like talking to S3) is considered egress traffic. It is like a sandboxed AWS service, that sits out there on its own. It really isn't any different than using Linode or Digitial Ocean for your compute resource and using AWS for block storage, queuing, DNS, etc.. Other AWS services can't "see" your Lightsail instance, like they can see your EC2 instances. You can't connect EBS volumes to it, you can't take advantage of elastic IPs, or anything of that sort. It really is a separate service that sits on its' own, under the comfort of the AWS name.
If I remember right, even tags don't carry over between Lightsail and the rest of your AWS account. Again, Lightsail is fine as a service, but it is only "sort of" in the AWS ecosystem. It mostly sits on its own as an isolated service, backed by AWS.