Update: answer has been reordered and extended.
General rules
A good answer concerning general rules for comparatives and superlatives is
"More clear" vs "Clearer": when to use "more" instead of "-er"?
- one syllable: add suffix -est or -er.
- many syllables: use most or more.
- two syllables and ends -y: change y to -iest or -ier
Lamer
The word lame has acquired new meanings in my lifetime which mean you can't use "lamer" to indicate the "more lame" without serious risk of being misunderstood.
Randomer
Randomest and randomer are not words in general use. I'd not use them. I'd say "most random" or "more random" - whilst feeling uneasy about my mathematical credentials.
Context is important
Before you can decide whether it is appropriate to use "random", "more random" or "randomer", you have to consider which meaning of random you are using and how formal the context is.
Oxford online says:
adjective
1 made , done , or happening without method or conscious decision:
apparently random violence
- Statistics governed by or involving equal chances for each item:
a random sample of 100 households
- (of masonry) with stones of irregular size and shape.
2 informal odd, unusual, or unexpected:
the class was hard but he was so random that it was always fun
In (very) informal use, it might well be acceptable to say something like "I saw the randomest thing on the way home!"
In ordinary use (outside maths), people do talk about degrees of relative randomness. We often talk of randomness as if it were a measure of disorder. So in this case we can say one thing is more random than another (meaning less ordered, or where the order is harder to discern).
I'm not a statistician so I don't know, but I suspect in statistics, random is an absolute. This means something is either random or it is not. There shouldn't be degrees of randomness. If you are a statistician writing a statistical paper you will know whether it is ever correct to write "more random".