  It has been known since \cite{Pgroupchunk} that any group definable in an
$o$-minimal expansion of the real field can be equipped with a Lie group
structure. It is therefore natural to ask when is a Lie group Lie isomorphic to
a group definable in such an expansion. Conversano, Starchenko and the first
author answered this question in \cite{COSsolvable} in the case when the group
is solvable. This paper answers similar questions in more general contexts.
  We first give a complete classification in the case when the group is linear.
Specifically, a linear Lie group $G$ is Lie isomorphic to a group definable in
an $o$-minimal expansion of the reals if and only if its solvable radical has
the same property.
  We then deal with the general case of a connected Lie group, although
unfortunately we cannot achieve a full characterization. Assuming that a Lie
group $G$ has a "good Levi descomposition", we prove that in order for $G$ to
be Lie isomorphic to a definable group it is necessary and sufficient that its
solvable radical satisfies the conditions given in \cite{COSsolvable}.
