It actually means "swallow". The correct word for a swallow in Czech is vlaštovka. But, because it was hard to spell for our ancestors, the "v" was put aside and they spelled it laštovka (or laštůvka, which is dialect). Because English people (or other foreigners) didn't know how Czech ortography works, they spelled the name as they heard it - Lastufka. So the way from "vlaštovka" (swallow) to Lastufka would be:
1 Vlaštovka
2 Laštovka / Laštůvka (variant form)
3 Laštůfka
4 Lastufka