  We propose a natural Fedosov type quantization of generalized Lagrange models
and gravity theories with metrics lifted on tangent bundle, or extended to
higher dimension, following some stated geometric/ physical conditions (for
instance, nonholonomic and/or conformal transforms to some physically important
metrics or mapping into a gauge model). Such generalized Lagrange transforms
define canonical nonlinear connection, metric and linear connection structures
and model almost Kahler geometries with induced canonical symplectic structure
and compatible affine connection. The constructions are possible due to a
synthesis of the nonlinear connection formalism developed in Finsler and
Lagrange geometries and deformation quantization methods.
