EpsContract[exp] handles contractions of two Levi-Civita tensors. It is also an option of Contract and other functions that specifies whether such contractions should be done or not.
LCD[\[Mu], \[Nu], \[Rho], \[Sigma]]
EpsContract[% %] // Factor2\overset{\text{}}{\epsilon }^{\mu \nu \rho \sigma }
(1-D) (2-D) (3-D) D
Contract[LCD[\[Mu], \[Nu], \[Rho], \[Sigma]]^2] // Factor2(1-D) (2-D) (3-D) D
Contract[LCD[\[Mu], \[Nu], \[Rho], \[Sigma]]^2, EpsContract -> False]\left(\overset{\text{}}{\epsilon }^{\mu \nu \rho \sigma }\right)^2