A structural study of the smaller Li$^+$He$_n$ clusters with $nle30$ has been carried out using different theoretical methods. The structures and the energetics of the clusters have been obtained using both classical energy minimization methods and quantum Diffusion Monte Carlo. The total interaction acting within the clusters has been obtained as a sum of pairwise potentials: Li$^+$-He and He-He. This approximation had been shown in our earlier study cite{8} to give substantially correct results for energies and geometries once compared to full ab-initio calculations. The general features of the spatial structures, and their energetics, are discussed in details for the clusters up to $n=30$ and the first solvation shell is shown to be essentially completed by the first ten helium atoms.
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