Various notions of approximation of locally compact groups by Lie groups have been studied in the literature, and there are indications that there is some danger of confusion. Therefore, the author undertakes a systematic comparison. A Lie-normal family in a locally compact Hausdorff group \(G\) is defined as a set \({\mathcal N}\) of normal subgroups with Lie factor groups and with trivial intersection. If such a family exists, then \(G\) is called weakly Lie-projective. If every neighborhood of the identity contains a member of \({\mathcal N}\), then \(G\) is said to be Lie-projective. If \({\mathcal N}\) consists of compact groups and is well-ordered by inclusion, then \(G\) is said to be countably Lie-projective. The latter two notions are characterized in various ways. E.g., \(G\) is countably Lie-projective if and only if it admits a countable Lie-normal family \({\mathcal N}\) which contains some compact group, and also if and only if it is Lie-projective and metric. \(G\) is Lie-projective if and only if \(G\) has a Lie-normal family \({\mathcal N}\) which contains some compact group, and also if and only if \(G\) is a locally compact projective limit of Lie groups. The author gives examples showing that in the following chain of implications, none can be reversed: Lie group \(\Rightarrow\) countably Lie-projective group \(\Rightarrow\) Lie-projective group \(\Rightarrow\) weakly Lie-projective group \(\Rightarrow\) locally compact Hausdorff group. -- As a consequence of these results, a further hypothesis should be added in \textit{J. Szenthe}'s paper [Acta Sci. Math. 36, 323-344 (1974; Zbl 0288.57022)] on Hilbert's fifth problem (characterisation of transitive Lie group actions), namely, the groups under consideration should be second countable.