I am analysing conflicting software requirements and I tried to apply lex specialis and lex posterior principles, but then I understood that the "the customer is always right" is the main principle. My question is - how to come up with the catchy Latin phrase for such "lex"? Google translate gives "in elit semper ius", but Google Search finds nothing suitable for such phrase. That may mean that the Google translation is not the best suggestion.
You could use "emptor" for "customer".
emptor (emt-), ōris, m. [emo], a buyer, purchaser (Lewis & Short)
For the "is always right" part, I would suggest the idiom "bene dicit". I think you could leave the "always" ("semper") out in Latin.
So "emptor bene dicit" (literally "the buyer speaks well") seems a reasonable translation to me.
The English "The customer is always right" is a sardonic concession: we do not, of course, really think that the customer is always right, but we have to pretend they are, because the rules say we are not to argue with the customer, but to do their bidding. It is not easy to create a succinct Latin expression that captures the irony well.
Therefore I would rather suggest:
Cum emptore non est concertandum.
One must not debate with the customer.
For emptor, see Laravel's answer. The temptation is great to say ... non est disputandum, in order to evoke the famous De gustibus non est disputandum, but in truth disputare, in Classical Latin at least, means to examine, treat of something, not to have an argument, so I chose concertare instead.
An alternative option would be:
Emptor semper vincit.
The customer always wins.
If you want, you can also say Semper vincit emptor, thus alluding to Omnia vincit amor (Love conquers all), which is a famous line from Vergil. By the way, we are used to thinking of vincere in a military sense (as in Veni, vidi, vici), but in truth it often simply means "prevail, outweigh," etc., so it is quite a good fit on its own.
And finally, an attempt to capture the irony/sarcasm of the English original:
Quidquid poscit emptor, id vere videlicet atque iure poscitur.
Whatever the customer demands, that is obviously demanded rightly and justly.
Videlicet means "obviously," and like its English equivalent is sometimes used ironically.