Lemmy lets you upload images, directly to lemmy.ml in your case.
Front-ends like Alexandrite (that I'm currently using) haven't integrated it yet - it only gives you the choice of URL, Its may be the same with Thunder - there's an active Community here
I am also curious. Especially whether there’s some Lemmy-specific feature, or if it’s just up to the way you connect, and some apps are integrating with an image service directly.
It varies by instance. Lemmy.ee has a low cap on image upload size because it's a small instance, but I think lemmy.world allows uploads of a larger size.
You can also use another image hosting site like imgur or pixelfed and link from those in the URL section of your post.