On a menu,
肘子 nearly always means 'pork hock/shoulder' — a classic banquet dish.
红烧肘子 (red-braised pork hock) and
东坡肘子 (Dongpo's pork hock, a Sichuan specialty named after the poet
苏东坡) are signature versions. The 'elbow' meaning survives only in colloquial speech;
胳膊肘 (gēbozhǒu) is the more common everyday word.