The suffix -lvë is the first person plural inclusive inflection: “we (including you)” (PE17/130; VT49/16, 51). The corresponding possessive form -lva “our (inclusive)” appears in its genitive form -lvo in the famous phrase elen síla lúmenn’ omentielvo.
Possible Etymology: Tolkien indicated that this inflection was ultimately derived from the primitive pronoun ✶we, with the same plural marker l as other plural inflections such as -l(yë) and -ltë, and that its oldest form was ✶-lwe (PE17/130; VT49/50-51). At one point Tolkien indicated that the change of lw > lv was the normal phonetic development in Quenya (PE17/129). There little evidence that Tolkien carried through with the phonetic rule, however, and there are plenty of examples of unmodified lw in later Quenya. A better explanation might be that -lwe changed to -lve under the influence of the independent pronoun ve. These ideas came out of a discussion with Shihali on the Vinyë Lambengolmor Discord Server (VLDS) on Jan 28, 2018.
Conceptual Development: @@@
-lmë 1st person pl. pronominal ending: "we" (VT49:38; 51 carilmë *"we do", VT49:16). It was originally intended to be inclusive "we" (VT49:48), including the person(s) spoken to, but by 1965 Tolkien made this the ending for exclusive "we" instead (cf. the changed definition of the corresponding possessive ending -lma, see above). _(VT49:38) Exemplified in laituvalmet "we shall bless them" (lait-uva-lme-t "bless-shall-we-them") (the meaning apparently changed from inclusive to exclusive "we", VT49:55), see also nalmë under ná# 1. (LotR3:VI ch. 4, translated in Letters:308_)