  We investigate so-called "higher" Siegel theta lifts on Lorentzian lattices
in the spirit of Bruinier-Ehlen-Yang and Bruinier-Schwagenscheidt. We give a
series representation of the lift in terms of Gauss hypergeometric functions,
and evaluate the lift as the constant term of a Fourier series involving the
Rankin-Cohen bracket of harmonic Maass forms and theta functions. Using the
higher Siegel lifts, we obtain a vector-valued analogue of Mertens' result
stating that the Rankin--Cohen bracket of the holomorphic part of a harmonic
Maass form of weight $\frac{3}{2}$ and a unary theta function, plus a certain
form, is a holomorphic modular form. As an application of these results, we
offer a novel proof of a conjecture of Cohen which was originally proved by
Mertens, as well as a novel proof of a theorem of Ahlgren and Kim, each in the
scalar-valued case.
