Latin (or Greek) -x becomes -ght?
These English words did not come from Latin. Rather, Latin and English both inherited these words from Proto-Indo-European (though not directly — there were intermediate languages). The nouns light and lux came from PIE *leuk-, while the adjective light came from PIE *le(n)gwh-. Night and nox came from PIE *nok(w)t-.
So, x did not become ght. Instead both of these words came from a language that existed about 5000 years ago; during those 5000 years, the pronunciations of the words changed many times.
It may be relevant to note that both night and light were pronounced with a /xt/ in Proto-Germanic (the language that came before Old English). It is only later on that the "gh" became silent.
(Etymology data came from etymonline.com.)
A correspondence between English '-ght' and Latin '-ex' is a bit fluid, given the vagaries of English spelling and historical phonetic and semantic drift in both Germanic and Italic and the different ways they divergesd from common Proto-Indo-European roots.
But to limit ourselves, the only three English/Latin pairs like this are night / nox, light / lux, and
right / rex.
(and this seems to have separated semantically more than the other two ('rex' = 'king' or ruler, from the past participle 'rectum' of 'rego' to rule.)
For other possible English-Latin pairs:
- 'eight' corresponds to 'octo' (no 'x')
- 'aught', 'naught', 'ought', 'fight', seem to be solely Germanic (see Etymonline for online references)
For Latin-English pairs:
- 'sex' corresponds to 'six' (no '-ght' in the Engilsh)
- 'lex' corresponds to 'law' (which are cognate
- 'crux' corresponds to 'cross'
- 'vox' corresponds to 'voice'
Whenever these are pairs, I've only given actual cognates, but the phonetic or spelling rules diverged from the ght/x pattern.