The tourists have failed to bowl out Australia once over the first two Tests, having long lost their world-beating reputation as the "Calypso Kings".
But Lehmann noted that they played well while still losing by 177 runs in Melbourne.
"I was really pleased the way they fought back, yeah, after being six for 90 day two and then obviously bat really well on day three," he said.
The West Indies crashed to an innings defeat in Hobart and lost the series on Tuesday in Melbourne, but captain Jason Holder and former skipper Denesh Ramdin both made battling half centuries.
Sydney Morning Herald cricket commentator Malcolm Knox also celebrated the West Indies finding their heart despite another defeat.
"Finally, the tourists showed some grit and in so doing mounted an argument for why their mooted demotion from Test cricket's top division would be a retrograde step," he wrote in a column published Wednesday.
"The longer they play in Australia, the more they learn and the better they get."
But ominously for the West Indies, Lehmann stressed Australia could still improve.
"I still think there's areas on any given time we need to improve on... No-balls this game for example," he said.
"I think our fielding was a lot better this game than it was in the previous couple of Test matches. Our batting's been very good all summer. It's coming together nicely but you're always aiming for perfection and trying to strive to be the best team you can be.
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