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I read a prediction that if the global fertility rate stayed at the same rate as it was in 1995 by 2150 the population would be 256 billion people. That sounds crazy, but for my sci-fi I'm rolling with it (albeit shaving off 50 billion).

The Hegemony needs to feed these 200 billion odd citizens. One solution I'm interested in is cultured meat/"lab meat". Can cultured meat be grown in a industrial scale? And would this scale be large enough to feed 200 billion humans. (Their diets would be supplemented with vertical farming and green houses)

Note: Only 30-50% of the population can be fed by traditional farming alone.

Not really.

Lab meat only replaces meat, which is only a small fraction of the global diet, and you still need to farm something to feed the lab meat, so there are few gains. That said someday it could easily become less wasteful than traditional ranching, by using plants and plant byproducts humans will not eat and even human garbage. Lab mean does not gain you much in terms of total calories however, because as I said you have to feed it something.

You are still going to use grains for the majority of your calories.

Really the globe could feed that population without much problem, the issue would be we would have to convert a much larger portion of the worlds surface into farmland, and start using water intelligently which is going to mean a lot of government oversigt. Aqua culture may be a bigger help than vat meat, since it is literally creating farmable surface.

Heck yah. I got yer lab meat factory right here!

https://www.alibaba.com/product-detail/Feed-additive-Brewer-dried-yeast-dry_60078544242.html

This robot factory grows yeast to use as a food supplement. The protein content is comparable to soybeans. You can easily enrich yeast with minerals and in fact this is widely done as the yeast makes the mineral nutrients more bioavailable.

The benefit of the yeast is you can grow them in three dimensions on any kind of land or even on boats at sea. The downside is that you need to provide the yeast with everything they need including a nitrogen source and organic carbon to make into their bodies. Soybeans can do a lot of that work on their own, out in a field, using the sun and obtaining their own carbon from the air but they grow only in one dimension and according to the season.

Yes (and it will happen fairly soon)

With the advent of 3d printers it's possible to print meat like products from other products.

Eventually society will have algae, bacteria and yeast tanks to produce the food we need. The only problem is it's not exactly appetizing. With additional processing, it can be made into products that have the look, taste and even smell of other foods including meat.

The tanks can be supplied with the required nutrients and water extracted from processed sewerage and output food and oxygen. Since algae is so fast growing and efficient, it could also replace vegetables as well as meat.

As best, real meat and vegetables would be the choice only for the ultra rich.