  In this paper we classify, under certain restrictions, all homogeneous
conformal subalgebras $\goth L$ of a lattice vertex superalgebra $V_\Lambda$
corresponding to an integer lattice $\Lambda$. We require that $\goth L$ is
graded by an almost finite root system $\Delta\subset \Lambda$ and that $\goth
L$ is stable under the action of the Heisenberg conformal algebra $\goth
H\subset V_\Lambda$. We also describe the root systems of these subalgebras.
The key ingredient of this classification is an infinite type conformal algebra
$\goth K$ obtained by the Tits-Kantor-Koeher construction from a certain Jordan
conformal triple system $\goth J$. We realize a central extension $\^{\goth K}$
of $\goth K$ inside the fermionic vertex superalgebra $V_\Z$, thus extending
the bozon-fermion correspondence.
