Brown dwarfs -- dim red stars that are too cool to burn hydrogen -- are very similar in appearance to red dwarf stars, which are just hot enough to burn hydrogen  Stars, when first formed, contain substantial amounts of the element lithium  All stars but the coolest of the brown dwarfs are hot enough to destroy lithium completely by converting it to helium
Accordingly, any star found that contains no lithium is not one of these coolest brown dwarfs
None of the coolest brown dwarfs has ever been hot enough to destroy lithium.