A Lie 2-groupoid is a 2-truncated ∞-Lie groupoid.
Every Lie groupoid is a special case of a Lie 2-groupoid.
For $A$ an abelian Lie group, its double delooping is a Lie 2-groupoid $\mathbf{B}^2 A$.
More generally for $G$ a Lie 2-group, its delooping $\mathbf{B}G$ is a one-object lie 2-groupoid
For $X$ a smooth manifold, the path 2-groupoid $\mathbf{P}_2(X)$ is a Lie 2-groupoid (a 2-groupoid internal to diffeological space)s.