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I haven't done too, too much in-depth research on this one, but a general search seems to show that this is a joke or a meme. Either way, I'm very interested in knowing a bit more about the context of this phrase when used like this.
As a side note, this was someone's name while playing an online game, if that relates to your response in any way.
次{つぎ}行{い}ってみよう is a famous phrase used by a Japanese comedian いかりや長{ちょう}介{すけ}. IIRC this phrase caught on in the late 1970's. He used this catchphrase frequently in his TV comedy show, at the end of many comedy bits.
(picture taken from here)
It literally means "Let's go to the next segment (scene, chapter, etc.)", which is not really funny by itself.
This phrase is almost forgotten by young people, but perhaps its main use today is to forcibly (yet jokingly) change the topic of a conversation. When someone started to talk about something that's not very interesting or convenient to someone, he may say 次いってみよう, and it works as the sign to forget everything that's currently taking place. (In a sense it's a humorous way to say "never mind".)
