  We construct a new class of exact solutions describing spacetimes possessing
Lie algebroid symmetry. They are described by generic off-diagaonal 5D metrics
embedded in bosonic string gravity and possess nontrivial limits to the
Einstein gravity. While we focus on nonholonomic vielbein transforms of the
Schwarzschild metrics to 5D ansatz with solitonic backgrounds, much of the
analysis continues to hold for more general configurations with nontrivial Lie
algebroid structure and nonlinear connections. We carefully investigate some
examples when the anchor structure is related to 3D solitonic interactions. The
approach defines a general geometric method of constructing exact solutions
with various type of symmetries and new developments and applications of the
Lie aglebroid theory.
