If you want to extract pure salt of REE you can reflux LnF3 or MLnF4 with aqueous 10% NaOH, separate Ln(OH)3, dissolve it in mineral acid and repeat this to obtain fluoride-free salt. I do not think that there is a solvent in which this compound will dissolve without destruction. Perhaps melts of alkali metal fluorides or something like liquid ammonia.
I expect NaLnF4 to be soluble in high-boiling-point nonpolar solvents such as oleic acid (OA), oleylamine (OM), and 1-octadecene (ODE). This has to be confirmed by solubility tests in these solvents.
A fluoride scavenger, such as boric acid (H3BO3), can be used in conjunction with HNO3 to obtain Ln nitrate solution. We use closed vessel microwave digestion to solubilize fluoride-bearing salt residues using HNO3 and a stoichiometric excess of H3BO3.
It is also noted that the resulting HBF4 can be removed from your sample by heating.