I'm thinking of brewing some hard lemonade, and from what I've read, I'll need to neutralize the yeast with sulfites if I want to prevent it from getting too dry. Will I need to force carbonate after that? Is there a way to make a sweet, carbonated, hard lemonade using natural carbonation / bottle conditioning?
The answer is similar to the one in this post, but the short answer is that your safest bet is force-carbonating.
The problem with bottle conditioning is that you've already killed most of your yeast, and even if you were to successfully repitch, there's really no good way to "turn off" fermentation when you reach your target carbonation.
There are also some potential issues with trying to stop fermentation halfway through - it would be best to ferment it fully to the alcoholic strength you want, let the yeast settle, rack, then add a stabilizer, and add sugar for sweetness at that point.
This way, the yeast will be able to clean up off-flavors at the end of the fermentation cycle, and you mitigate risks of the campden/sulfites not fully neutralizing the entire yeast population.
Once you sulfite the lemonade to neutralize the yeast you cannot bottle condition. The sulfite will prevent any further fermentation which is necessary for bottle conditioning. The only option is to force carbonate. Although you could bottle still and add charged water to add fizz or bottle condition the dry lemonade and then sweeten at the time of drinking.
If you want natural carbonation your best bet is to find a yeast will naturally low attenuation.
For example White Labs WLP720 is a wine/mead yeast to make sweet wines and mead as the attenuation is less than 75%.
I don't know how well it will go with your lemonade. You could also try looking for sweet cider yeasts I think Wyeast may do something like that.