The problem is that what you're placing as your formula in the cell is exactly what is between the quotes.
Let us assume LookupValue contains "f100". The way you have your variable set up, your active cell's formula would read:
=VLOOKUP(lookupvalue,Error84,10,false)
Another issue is Error84 a named range with at least 10 columns? I'll assume that it is.
Your code would be:
Code:
ActiveCell.Formula = "=VLOOKUP(" & LookupValue & ",Error84,10,false)"
Note that the LookupValue containing the string you want (in this case "f100") added is outside your literal string quotes now. The formula in the cell would then read:
=VLOOKUP(f100,Error84,10,false)