Conditional formatting cannot "see" inside of the execution of a function like this. A couple of approaches:
1) Include something in the output of the function that will indicate which table it came from. Maybe something like =IFERROR(IFERROR("a"&VLOOKUP(C2,'New Held Batches Sheet'!$C$5:$D$5,2,0),IFERROR("b"&VLOOKUP(C2,'New Held Batches Sheet'!$C$8:$D$22,2,0),"c"&VLOOKUP(C2,'New Held Batches Sheet'!$C$25:$D$35,2,0))),""). If you still need the conditional formatting, then you can have your conditional formatting check for the leading character (a, b, or c) and format accordingly. The main thing I don't like about this approach is that it adds a piece of information to the result, which could cause difficulties for other formulas that need this result.
2) (My personal favorite) Use helper cells to return the result from each lookup. cell1 =VLOOKUP(C2,'New Held Batches Sheet'!$C$5:$D$5,2,0) cell2 =VLOOKUP(C2,'New Held Batches Sheet'!$C$8:$D$22,2,0) cell3 =VLOOKUP(C2,'New Held Batches Sheet'!$C$25:$D$35,2,0). Then a 4th cell could look at those three and return the value from the cell that is not N/A, and your conditional formatting could look at those three cells and format according to which one is not N/A.
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