  We determine the properties of generalised parton distributions (GPDs) from a
lattice QCD calculation of the off-forward Compton amplitude (OFCA). By
extending the Feynman-Hellmann relation to second-order matrix elements at
off-forward kinematics, this amplitude can be calculated from lattice
propagators computed in the presence of a background field. Using an operator
product expansion, we show that the deeply-virtual part of the OFCA can be
parameterised in terms of the low-order Mellin moments of the GPDs. We apply
this formalism to a numerical investigation for zero-skewness kinematics at two
values of the soft momentum transfer, $t = -1.1, -2.2 \;\text{GeV}^2$, and a
pion mass of $m_{\pi}\approx 470\;\text{MeV}$. The form factors of the lowest
two moments of the nucleon GPDs are determined, including the first lattice QCD
determination of the $n=4$ moments. Hence we demonstrate the viability of this
method to calculate the OFCA from first principles, and thereby provide novel
constraint on the $x$- and $t$-dependence of GPDs.
