That's the general question. More concretely, here
c' is linked to C4 (middle C). Now, what is the Lilypond absolute representation for G5 in G major key?
LilyPond's input is key-independent. While in equal-tempered tuning the absolute pitch of C sharp and D flat are the same, the musical/scale function is different. Scientific pitch notations usually retain that difference even though basically all keyboards (and the Midi standard) drop it.
LilyPond also retains that difference and preserves it even when transposing: transposing does not change the relative scale positions.
In short, LilyPond's absolute
c' is C4, always. Absolute
g'' is G5, always. Absolute
cis''' is C#6, always. Absolute
des, is Db2, always. How those pitches print (namely which accidentals are printed along with them) depends on preceding accidentals in the measure, on the key signature, and on the accident style setting (baroque style repeats a lot more accidentals than modern style does).