  We generalise a result from [Bak15] on K3 type hyperk\"ahler manifolds
proving that a line in a lagrangian plane on a hyperk\"ahler manifold $X$ of
Kummer type has Beauville-Bogomolov-Fujiki square $-\frac{n+1}{2}$ and order 2
in the discriminant group of $H^2(X,\mathbb{Z})$. Vice versa, an extremal
primitive ray of the Mori cone verifying these conditions is in fact the class
of a line in some lagrangian plane. In doing so, we show, on moduli spaces of
Bridgeland stable objects on an abelian surface, that lagrangian planes on the
fibre of the Albanese map correspond to sublattices of the Mukai lattice
verifying some numerical condition.
