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A new model of DBI inflation is introduced where the mobile brane, the inflaton field, is moving relativistically inside a Lifshitz throat with
the arbitrary dynamical exponent $z$. The dependence of physical observable quantities, such as the spectral index, the ratio of the tensor to scalar
amplitudes $r$ and the non-Gaussianity parameter $f_{NL}$, are calculated a functions of the exponent $z$. Depending on the value
of $z$ and the form of the inflaton potential the curvature perturbations can be red-tilted, scale invariant, or blue-tilted and significant
amounts of non-Gaussianities can be produced.
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