I believe so.
Although given his character traits it's possible he was never in Vietnam and held onto the lie as a way to get attention or to justify his anger at elements of society. I've seen the movie many times though, and I don't think there's anything in there that would support the theory beyond a doubt.
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The Big Lebowski was released in 1998.
The Production Budget for The Big Lebowski was $15,000,000.
The Big Lebowski grossed $17,498,804 in the domestic market.
The Big Lebowski... he had "Bunny Lebowski" and a "Nihilist" floating in his pool.
Maude Lebowski (Julianne Moore) in Big Lebowski