  We describe a new large class of Lorentzian Kac--Moody algebras. For all
ranks, we classify 2-reflective hyperbolic lattices S with the group of
2-reflections of finite volume and with a lattice Weyl vector. They define the
corresponding hyperbolic Kac--Moody algebras of restricted arithmetic type
which are graded by S. For most of them, we construct Lorentzian Kac--Moody
algebras which give their automorphic corrections: they are graded by the S,
have the same simple real roots, but their denominator identities are given by
automorphic forms with 2-reflective divisors. We give exact constructions of
these automorphic forms as Borcherds products and, in some cases, as additive
Jacobi liftings.
