The only free and comprehensive online etymological dictionary of the Spanish language
llevar (Verb) "to carry;" "to wear"
10th cent. Old Spanish levar. From Latin levare "to raise," from levis "light" (see leve).
Indo-European
Romance
Portuguese levar,, Catalan llevar, French lever, Italian levare, Aromanian ljeau, Romanian lua, Sardinian leài

The present tense stem was liev-, which became llev-. Ll- then replaced li- in all other conjugal forms of the verb by analogy.