You can install the package "lxde" from Synaptic package Manager or Software Manager. This is the meta package for the LXDE desktop. After installation, you will be able to choose the LXDE desktop at log in from the same list that includes Gnome 3, Mate, etc.
This will not be the pure LXDE desktop, some Gnome apps will continue to run in the background and many will show up in the LXDE menu. To experience the true LXDE environment, you really should do a fresh installation of the Mint LXDE version.
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