In this paper we consider the notion of $\Cal I^*$-uniform equal convergence introduced by Das, Dutta and Pal [15] and two related notions of convergence, namely, $\Cal I^*$-uniform discrete and $\Cal I^*$-strong uniform equal convergence. We then investigate some lattice properties of $\Phi^{\Cal {I^*}-ue}$, $\Phi^{\Cal {I}^*-ud}$, $\Phi^{\Cal {I}^*-sue}$, the classes of all functions defined on a non-empty set $X$, which are $\Cal I^*$-uniform equal limits, $\Cal I^*$-uniform discrete limits and $\Cal I^*$-strong uniform equal limits of sequences of functions belonging to a class of functions $Phi$ respectively.