  We work out the exact relationship between algebraic modular forms for a
two-by-two general unitary group over a definite quaternion algebra, and those
arising from genera of positive-definite quinary lattices, relating stabilisers
of local lattices with specific open compact subgroups, paramodular at split
places, and with Atkin-Lehner operators. Combining this with the recent work of
R\"osner and Weissauer, proving conjectures of Ibukiyama on Jacquet-Langlands
type correspondences (mildly generalised here), provides an effective tool for
computing Hecke eigenvalues for Siegel modular forms of degree two and
paramodular level. It also enables us to prove examples of congruences of Hecke
eigenvalues connecting Siegel modular forms of degrees two and one. These
include some of a type conjectured by Harder at level one, supported by
computations of Fretwell at higher levels, and a subtly different congruence
discovered experimentally by Buzzard and Golyshev.
