Is there a non-destructive way to replace water in meat such as chicken or beef, with another liquid (e.g. lemon juice)?
No, there isn't. And you're probably not actually asking the question you mean to ask.
The first problem is that, to a first approximation, lemon juice is water—approximately 92%. Chicken breast is approximately 64% water, so even if you could remove that 64% water and replace it with lemon juice, you'd get chicken with 59% water and 5% sugar and other lemon juice components. It's rather silly to remove all the water, when your end result is to reduce it a small amount.
The second problem is that the chemistry inside the cells in the meat depends on that water. Removing it would destroy the meat—the cells would all collapse and likely eject their contents, proteins would be denatured in weird ways or broken apart, etc. Even beef jerky, which you'd think of as dry, is approx. 23% water. Flour is approx. 12%. Dried rice, 10%. You're asking for drier.
Likely, what you're actually trying to do—at least, if you're cooking, not performing chemistry experiments—is get lemon flavor into your chicken. In which case, obvious ways are marinade, flavor injectors, and squeezing it on after cooking the chicken.
I'm no expert (at all!), but I would go about this by first dehydrating the meat then rehydrating with the desired liquid. I would dehydrate the meat in a dehydrator or if you don't have one a low oven. A dehydrator would be better as it would remove a higher percentage of water content but an oven would do. I would then soak the meat in the desired liquid although 2 things could go wrong here: the meat losing its texture (likely) and not soaking up all the liquid just it's water content. This is the best I can of but I hope it helps.