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).
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.