Τhe verb "ψεύδομαι" is an ancient Greek verb and it means "Ι am telling lies".
In modern Greek it has survived with the same meaning, but it is used only in formal circumstances (ex.in a court, or in the parliament).
The future tense in ancient Greek is "ψεύσομαι" or "ψευσθήσομαι", but none of these two forms is used in modern Greek.
In modern Greek you can form only the future continuous "θα ψεύδομαι", but it sounds very formal.
‘I deceived him’ = "Τον εξαπάτησα" (formal) οr "Τον κορόιδεψα" (informal) οr "Tου την έφερα" (slang).
‘I don’t want to lie to you’ = "Δε θέλω να σου λέω ψέμματα" (informal, but can be used in formal occasions).