lance (n.) Look up lance at
late 13c. (late 12c. as a surname), from Old French lance "spear, lance, lance-length" (12c.), from Latin lancea "light spear, Spanish lance" (Italian lancia, Spanish lanza), a word said by Varro to be of Spanish origin, hence possibly from Celt-Iberian. The French word spread generally into the Germanic languages: German Lanze, Middle Dutch lanse, Dutch lans, Danish landse.

Lance corporal "private soldier performing the duties of a corporal" (1786) is a folk-etymology or partial nativizing of obsolete lancepesade "officer of lowest rank" (1570s), which is an Englishing of Old Italian lancia spezzata "old soldier," literally "broken lance."
lance (v.) Look up lance at
"to pierce with a lance," c. 1300, from Old French lancier "to throw forward, hurl, dash; attack with a lance," from Late Latin lanceare "wield a lance; pierce with a lance," from lancea (see lance (n.)). The surgical sense (properly with reference to a lancet) is from late 15c. Related: Lanced; lancing.