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For a t-norm T on a bounded lattice $(L,\le )$, a partial order ${\le }_T$ was recently defined and studied. In [11], it was pointed out that the binary relation ${\le }_T$ is a partial order on $L$, but $(L,{\le }_T)$ may not be a lattice in general. In this paper, several sufficient conditions under which $(L,{\le }_T)$ is a lattice are given, as an answer to an open problem posed by the authors of [11]. Furthermore, some examples of t-norms on $L$ such that $(L,{\le }_T)$ is a lattice are presented.