lance / launce are similar-sounding terms with different meanings (referred to as homophones). To better understand the differences, see below for definitions, pronunciation guides, and example sentences using each term. 👇
lance: (verb) move quickly, as if by cutting one's way. (verb) pierce with a lance, as in a knights' fight. (verb) open by piercing with a lancet.
launce: NA
lance: l·AE·n·s
launce: NA
(Examples are Wikipedia snippets under the CC ShareAlike 3.0 license. Definitions drawn from WordNet.)