I'd say the lab-grown variety will have a harder job to get public acceptance than the more conventional approach being taken by others, which is alluded to earlier, in particular the use of plant-sourced proteins (particularly from peas) along with other components to make an apparently highly realistic meat substitute.
I heard an interview earlier this year with the founder of a company called Beyond Meat, who argues that rather than trying to convert people to full vegetarianism (with the nos. of vegetarians remaining fairly static over the past 20 years), the better approach is to encourage people to substitute at least one or more meat-based meals to meatless; he saw his products as being part of this strategy, in that they are so 'meat-like' but have so many benefits of not being made of meat (health, environmental etc). . May have been this podcast? [Edit - no, it was this Nat Rad podcast from a couple of months ago.]
There's also the company Impossible Foods, which has picked up on the work of the NY chef who produced the Impossible Burger, as discussed in a Nat Rad podcast. This company has sourced significant funding from people like Bill Gates, so clearly there are some that see this is (part of) the future.
As a vegetarian, I'm not convinced I'd be too keen on something that replicates meat too accurately; I do like some meat substitutes such as saitan (a simple gluten-based product) that's excellent for making the most tasty homemade sausages, but given I've not eaten meat for well over twenty years I think that close to the real deal may be too much!
Edit: here's an extract from the Nat Rad link above re the Beyond Meat burger:
They took an MRI of a hamburger and looked at its interwoven protein and fat structure. [...]
In Beyond Burgers, fats and protein are bound through an extrusion process to create a pattie that has no cholesterol, half the saturated fat of hamburger and is soy-free.
The burger's main ingredient is Canadian yellow pea. It also contains coconut oil and canola oil, beetroot juice for colour, bamboo fibre and potato starch for binding and some flavouring.