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Not sure it's best practice and it was only for small scale docker things but I have in the past either used timestamps as tags, or skipped tags all together and just used the full image shas (If lambda supports that)

Yes, using the `shas` is what I want, maybe I wasn’t clear: Should I update the pulumi source code everytime I release a new image? This would make the build process somewhat strange, as the new images is built and pushed in the same repository just before calling pulumi.

Or would I figure out the sha to use dynamically in the pulumi program?

I would not change source code. If you can work it out in the program that's probably nicest, but if thats not doable I would pass them in as config values.