I also think this is a lot less likely to happen with meat. With diamonds part of the value is in signalling status. As such there is little incentive for customers to want to participate in driving down the price.
With lab-grown meat there will eventually be a number of outright benefits.
Lab-grown meat will no-doubt eventually become a common ingredient once it is economically viable. However it'll likely start off in highly processed foods where consumers are not especially discerning or seeking to signal status through consumption. This would include products like ready-made frozen meals and fast food.
It may eventually enter fine dining, but it won't obtain market dominance in our life times. People just get too set in their ways as they age, for instance the elderly in Japan drive demand for Whale meat. Older people tend to have the disposable income required for fine dining.