Hi - The breeding season for meadowlarks runs from May 10 to August 24, so we're beyond their estimated date range at this point. But given a 25 day egg-laying to fledging period, we're not beyond the point at which a pair could still be brooding or feeding fledglings. They on average produce 1 - 2 broods per year, so it would be relatively unlikely that a pair would lay a clutch and still be doing their parenting business this late in the season. But every estimate has a tail end that could in theory drag well beyond the average -- those outliers in the population.
So, the longer you can delay mowing without significantly impacting whatever you intend to do with the land, the less likely you are to disturb breeding pairs or young birds. It is impossible to provide a specific date. Just do the best you can.