The LREE mineral accumulations are characterized by monazite- and bastnaesite-type primary deposits in carbonatites and alkaline magmatic complexes, getting transformed into rhabdophane under neutral and alkaline pH condititions and into APS minerals such as florencite-Ce or La under pH lower than 7. HREE are concentrated in xenotime-type carbonatites and alkaline magmatic complexes while getting converted into churchite in secondary occurrences. It is a function of ionic radii.
I have no idea what your question is related to. The answer, which Dr. Dill provided, is a special case and thus I add some other information related only to magmatic rocks:
Basaltic rocks are formed in the Earth's upper mantle, which is essentially composed of olivine (Ol), orthopyroxene (Opx), clinopyroxene (Cpx) and spinel or garnet (Grt) and, sometimes, amphibole (Amp) and phlogopite (Phl). All REE are incompatible for these elements, which means that, upon partial melting, they will preferentially enter the melt. The exception is Grt for which the heavy REE (Dy - Lu) are less (Dy) or more (Lu) compatible. Among the major elements in magmatic rocks, the REE may best substitute for Ca, which in mantle minerals, is essentially hosted by Cpx and Amp.
During partial melting of the mantle, Cpx and Amp will preferentially enter the melt over Ol and Opx. Hence, the mantle residue will become enriched in these two minerals.
LREE over HREE enrichment will be controlled by the degree of partial melting. Small degrees of partial melting will produce melts with high LREE/HREE ratios because LREE are much more incompatible for the mantle minerals than the HREE. This is why continental alkali basalts (or ocean island basalts) are usually strongly enriched in LREE over HREE. This effect will be increased by residual Grt in the mantle which will hold back the HREE.
Increasing the degree of partial melting will lead to lower relative enrichments of LREE over HREE in the melt because most LREE have already entered the melt earlier. Therefore, mid-ocean ridge basalts have usually much lower LREE/HREE ratios and the residual mantle is strongly depleted in all REE because most or all Cpx and Amp have entered the melt.
In summary, all REE in all basalts are usually enriched over their concentrations in the mantle source. This is true even if Grt is a residual mineral in the source because Grt is commonly a minor mineral only and cannot hold back all HREE.
If you see chondrite-normalized or primitive-mantle-normalized REE patterns for mid-ocean ridge basalts you will see that very often they are depleted in the lightest REE (La, Ce, Pr, Nd) over the other REE. This is usually ascribed to their mantle source having already suffered from an earlier partial melting event that already removed part of the LREE.
Magmatic processes in rocks of the continental crust are more complicated. In granites, for example, trace minerals such as monazite, allanite or xenotime may become important hosts for the REE, despite their low abundances. Modeling their petrogenesis is thus not easy.
In crustal rocks you may see "anomalous" values for Eu in normalized REE diagrams. This is usually explained by the observation that a small portion of Eu in melts may be divalent and Eu2+ may become compatible for calcic plagioclase. "Negative Eu anomalies" may then indicate that the crustal residual source rock or, for examples, a granite, may be rich in Ca-plagioclase and held back Eu2+.