Tulips came to Europe from their native Turkey in the 16th century, so not surprisingly their name comes from a Turkish word: tulbant or tulibant. This word did not originally designate the flower, however; it is simply the Turkish word for "turban". The open flower of a tulip was thought to resemble the headgear.
But whereas the name for the flower came directly into the western European languages from Turkey, retaining the original "l", the name for the hat took a more circuitous route and acquired an "r" along the way. It is possible that the people of southwestern India, or the Portuguese who colonized parts of India, changed tulbant into turbant. This eventually became our turban. Fortuitously, really, because it would be very odd to read about people wearing tulips on their heads.