Complete Lattice, Complemented Lattice, Modular Lattice of Subspaces of a Vector Space
Hints:
The meet of a family is the intersection. The join is the sum.
Take a basis of $V/V_1$ and lift it to $V$.
Take an element of $V_1 \cap (V_2 + V_3)$. That you can write it as both $v_1 \in V_1$, and $v_2 + v_3$ for $v_2 \in V_2$ and $v_3 \in V_3$. That means that $v_2 = v_1 - v_3 \in V_1$.