We introduce the notion of relative co-annihilator in lattice equality algebras and investigate some important properties of it. Then, we obtain some interesting relations among $\vee$-irreducible filters, positive implicative filters, prime filters and relative co-annihilators. Given a lattice equality algebra $𝔼$ and $𝔽$ a filter of $𝔼$, we define the set of all $𝔽$-involutive filters of $𝔼$ and show that by defining some operations on it, it makes a BL-algebra.