You can add up values found by two or more VLOOKUPs in the same formula assuming they are all numbers and there are no errors. However, for search functions such as VLOOKUP to work as intended, you need to have the same names to be used in both search formulas and the sheets being searched through except the capitalizations.
This implies a significant problem in your existing setup which is the respective names for most ingredients in the recipe sheets not being the same as those in the ordering guide sheet. For example, Maldon salt is called “Salt, Maldon” in the ordering guide sheet but “Maldon Salt” in the Pizza Dough recipe sheet. While both of these names might appear as nearly the same to a human, they are quite different to Numbers.
To fix this, for example, you should use the same name for Maldon salt everywhere including the ordering guide sheet. If you need to have a different name in the ordering guide sheet than in the recipe sheets, then you may add a (hidden) column before the “Description” columns in the ordering guide sheet, have the cells in these columns carry the same ingredient names as in the recipe sheets and use those to search for Maldon salt in the recipe sheets.
The other potential problem for you could be a too high number of recipes which could lead to too long search formulas. You need as many VLOOKUPs as the number of recipe sheets in each “Amount to Order” cell formula in the ordering guide sheet to get the correct total for an ingredient. I think a formula with ten to fifteen VLOOKUPs might be manageable and stay within the formula length limit Numbers impose (not sure what the limit in Numbers is but I reckon it is not as high as the 16k characters limit for a formula in Excel).
Note that you could avoid manually creating a different search formula for each ingredient in the ordering guide sheet if you use the absolute referencing wisely. After creating a proper formula for only one of the ingredients, you can copy & paste it to all other “Amount to Order” cells in the ordering guide sheet to get the total for each ingredient.
If you actually run into the problem of too-long formulas in the ordering guide sheet, you may consider having more than one recipe in one sheet and using the SUMIF or the SUMIFS functions instead of VLOOKUP.