  We establish a theory of scalar Fourier coefficients for a class of
non-holomorphic, automorphic forms on the quaternionic real Lie group
$\mathrm{U}(2,n)$. By studying the theta lifts of holomorphic modular forms
from $\mathrm{U}(1,1)$, we apply this theory to obtain examples of
non-holomorphic cusp forms on $\mathrm{U}(2,n)$ whose Fourier coefficients are
algebraic numbers.
