"Eggness"?

Why do people say 'lemon-juice message' and 'eggness'?

Do they? In what context? I know that you can use lemon juice as "invisible ink" - you can't see what has been written until you heat the paper or paint it over with iodine. So a
'lemon-juice message' could be a secret message decodable only by someone who knew how. Does that fit the context in which you have heard it?

Eggness, even more than "lemon-juice message," needs some context. Eggs have many properties which, if not unique, are at least characteristic. But in any case the word is not a phrase.

["Eggness" - never heard it: could be it has something to do with "Eggs is eggs." Perhaps someone across the pond (a trans-ponder?) would atempt to explain this phrase. - B.]

I saw an example from The Mysterious Benedict Society and the Perilous Journey:

"Did the captain come?" Reynie asked. "Or did I dream that?"
"No, he came by this morning. Do you not remember? You sat up and something like 'eggness', then fell back to sleep."

In this instance, it appears that "eggness" isn't a word at all. The character specifically doesn't say that Reynie said "eggness", only that s/he, in a state of semi-consciousness, mumbled something unintelligible that *sounded like* "eggness", just as people roused out of sleep sometimes say something that sounds like "hufflewump" or "korbleworble." (VSD)