The verb traditionally used here is "to run." Yes, it's strange, it's just an idiomatic phrase. "Richard Nixon ran for President in 1960 and lost. In 1964 he did not run. But in 1968 he ran again and won." The term for the actual activities is similar in English and Spanish: "campaign" in English, "campaña" in Spanish. I can guess from the English spelling that we borrowed this word from French. The G isn't pronounced. The second syllable is pronounced just like "pain." "Lanzar" by itself translates into "to launch." "Launch" is the traditional word for putting a boat into the sea for its first trip. "To launch" can generally mean "to start something big and important." Apple "launches" a new iPhone with a big announcement, lots of ads, etc. To repeat, in English we would say someone is "running for President." We would never say someone "launched themselves." But we could refer to the start of the campaign by saying he "launched his campaign."