Does the word "chuunibyou" originate from the anime "Chuunibyou"?
No, the word "chuunibyou" was not coined by the anime Chuunibyou demo Koi ga Shitai! (nor by Black Lagoon). The term is attested back to 1999. (For further reading, the TVTropes article linked in Aki Tanaka's comment seems good.)

Data from Google Trends seem to indicate that searches for this word were low but slowly rising until October 2012, when searches spiked (because that's when Chuunibyou demo Koi ga Shitai! premiered). Search volume for "chuunibyou" has since fallen off, but is somewhat higher than it was just before October 2012, even after you subtract out searches specifically for Chuunibyou demo Koi ga Shitai!. My point here is that in 2006 (unlike now), the word "chuunibyou" had very limited purchase and it is hence unsurprising that it would not be used in Black Lagoon.