From the company website - it's vee'-lee-air
Both Wilier and Triestina were inspired by Italian patriotism following the World Wars. Wilier is an acronym. W is an abbreviation for the word Viva, which means “Long live”, beginning the phrase: W l’Italia liberata e redenta – Long live Italy, liberated and redeemed. It is pronounced /Vee’-lee-air/.
Let's hope your shop owners know more about bikes
Edit: I noticed kaisersling got it right. You get a free cigar from both shop owners