I have often found the following lemma of Bjorner, Eidelman and Ziegler to be useful:

Let $P$ be a bounded poset of finite rank such that, for any $x$ and $y$ in $P$, if $x$ and $y$ both cover an element $z$, then the join $x \vee y$ exists. Then $P$ is a lattice.

See Lemma 2.1 "Hyperplane arrangements with a lattice of regions", Discrete and Computational Geometry, Volume 5, Number 1, 263--288.

The hypothesis that $P$ is bounded means that $P$ has a minimal and maximal element. In fact, this hypothesis is slightly stronger than necessary: One can show that if $P$ has a minimal element and the other hypotheses hold then $P$ has a maximal element.

I have often found the following lemma of Björner, Eidelman and Ziegler to be useful:

Let $P$ be a bounded poset of finite rank such that, for any $x$ and $y$ in $P$, if $x$ and $y$ both cover an element $z$, then the join $x \vee y$ exists. Then $P$ is a lattice.

See Lemma 2.1 "Hyperplane arrangements with a lattice of regions", Discrete and Computational Geometry, Volume 5, Number 1, 263--288.

The hypothesis that $P$ is bounded means that $P$ has a minimal and maximal element. In fact, this hypothesis is slightly stronger than necessary: One can show that if $P$ has a minimal element and the other hypotheses hold then $P$ has a maximal element.