It has been known since (Pillay, J. Pure Appl. Algebra 53 (1988), no. 3, 239–255)that any group definable in an o $o$ -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 (Conversano, Onshuus, and Starchenko, J. Inst. Math. Jussieu 17 (2018), no. 2, 441–452) 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 $G$ is Lie isomorphic to a group definable in an o $o$ -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 $G$ has its Levi subgroups with finite center, we prove that in order for G $G$ to be Lie isomorphic to a definable group it is necessary and sufficient that its solvable radical satisfies the conditions given in (Conversano, Onshuus, and Starchenko, J. Inst. Math. Jussieu 17 (2018), no. 2, 441–452).