QUESTION: Let $\Lambda\times\Lambda\rightarrow {\Bbb Z}$ be a lattice,
that is, ${\Bbb Z}^n$ with a non-degenerate integer quadratic form, not 
definite, not necessarily unimodular, $n>2$. I want to show that for each $N>0$
there exists a 2-dimensional primitive sublattice $\Lambda_0\subset \Lambda$, 
also not definite, such that all vectors $x\in \Lambda_0$ satisfy $|(x,x)| > N$.

This question is motivated by considering a K3 surface 
(or a hyperkahler manifold) with 2-dimensional Picard
lattice. It is known that the squares of minimal rational
curves are bounded, and we want to find a manifold with
Picard number 2 having no minimal rational curves.