Jun Fukuyama obviously has a Japanese accent, and we don't necessarily know about Johnny Yong Bosch's Japanese accent from the Code Geass dub alone. Regardless, I'm talking about the character Lelouch from Code Geass, specifically when Lelouch has been masquerading as Zero from Season 1 Episode 1 until half of Season 1 Episode 12.
In Episode 12, everyone is surprised Lelouch/Zero isn't Japanese when Zero confirms Kirihara's guess (I originally watched the sub and not the dub, but I recall it went similarly in the sub, where I recall I thought 'They really thought Zero's Japanese?'). Does this mean that for the past 12 episodes, Lelouch, as Zero, had been speaking perfectly fluent Japanese with a Japanese accent, which he learned from his days with the Kururugi family and his other days in Japan thereafter probably with Sayokopter? If so, then is there any indication that he indeed had been speaking Japanese fluently with a Japanese accent? I believe that Lelouch is definitely N1 JLPT-level, but I'm not sure that means he has a Japanese accent, much like how not all fluent English speakers have an English (whether British, American, Britannian or European) accent.
My guess for the accent:
Since no one has suspected Zero is not Japanese whenever Lelouch, as Zero, has spoken Japanese publicly during the first 12 episodes, it follows that he, as Zero, must have had a Japanese accent while speaking Japanese in the first 12 episodes (and thereafter). Also, the indication may come after episode 12: If he later spoke Japanese publicly, then presumably he had a Japanese accent all along unless he had recently obtained one.
Alternatively, if Lelouch, not as Zero, has a Japanese accent when speaking Japanese, then of course Lelouch, as Zero, will have a Japanese accent when speaking Japanese.
Other possibilities include voice distortions like in Death Note (I don't think there was indication of this) or that Lelouch has come to mainly speak with a Japanese accent even when speaking English, as some kind of force of habit.
To compare Raye Penber from Death Note speaks Japanese, but his accent isn't Japanese, as Light pointed out. I like how the nationalities were pointed out like this even though the American characters in Death Note had their lines delivered in Japanese. Given that some other anime had addressed accents, I consider Code Geass unrealistic in this regard if Code Geass has not addressed things like this i.e. if indeed there isn't an indication of an accent, but of course, Lelouch had stayed in Japan more than Raye Penber had.