From the above, I conclude that either you or a third party runs a Lightning node you connect to, server-side, and which generates the invoice whose pre-image clients use as seeds. Therefore, it's entirely possible for the entity that controls the Lightning node to pass an invoice with non-random pre-image. Isn't that correct?


Nope its not correct, you don't understand. I explained it above, go and read that.

Not even how the data flows.

Read my previous answers.

Read the lightning specification ->  https://github.com/lightning/bolts/blob/master/00-introduction.md

Read the source code of a lightning node implementation -> https://github.com/lightningnetwork/lnd is pretty good also https://github.com/ACINQ/eclair

Read about preimages there. If you still feel like coming back here and garble hurr durr my seed isn't truly random & verifiable please do back your claims with data, code snippets, verifications, etc.

Repeat yourself all you want, rephrase yourself all you want, I don't care. You asked a question and got an answer.

Also, for the readers out there:

This person is alluding to the fact that  ANY developer can openly tamper with the various implementations of the protocol to get something that they want.

If that was a thing there would be bigger stuff to fish rather than developing an app where the max bet is ...$9 and every single one of us would have WAY more things to worry about.

You genuinely sound very schizo pal, I'm sorry to say this.