  Let $E=\mathbb{Q}\big(\sqrt{-d}\big)$ be an imaginary quadratic field for a
square-free positive integer $d$, and let $\mathcal{O}$ be its ring of
integers. For each positive integer $m$, let $I_m$ be the free Hermitian
lattice over $\mathcal{O}$ with an orthonormal basis, let $\mathfrak{S}_d(1)$
be the set consisting of all positive definite integral unary Hermitian
lattices over $\mathcal{O}$ that can be represented by some $I_m$, and let
$g_d(1)$ be the least positive integer such that all Hermitian lattices in
$\mathfrak{S}_d(1)$ can be uniformly represented by $I_{g_d(1)}$. The main
results of this work provide an algorithm to calculate the explicit form of
$\mathfrak{S}_d(1)$ and the exact value of $g_d(1)$ for every imaginary
quadratic field $E$, which can be viewed as a natural extension of the
Pythagoras number in the lattice setting.
