Let FG be the group ring of a group G over a field F whose characteristic i
s p not equal 2. Let * denote the involution on FG which sends each group e
lement to its inverse. Let (FG)(+) and (FG)(-) denote, respectively, the se
ts of symmetric and skew elements with respect to *. The conditions under w
hich the group ring is Lie n-Engel for some n are known. We show that if ei
ther (FG)(+) or (FG)(-) is Lie n-Engel, and G is devoid of 2-elements, then
FG is Lie m-Engel for some m. Furthermore, we completely classify the rema
ining groups for which (FG)(+) is Lie n-Engel.