If you are a lamb lover like me, choose better than me where you live. Lamb is popular in the north, particularly Inner Mongolia, and in the west of the country; much less so in the South and east where people often consider it to have an off-putting, rank smell.
It is usually known as 羊肉 (yáng ròu) but that term also includes mutton and goat. To be more sure of getting lamb and not some elderly sheep, you can try using 羊羔 (yáng gāo) or 小羊 (xiǎo yáng). If you see 山羊肉 (shān yáng ròu, literally mountain sheep meat), you've found goat - fine meat in my opinion.
Then you have the butchery problem. You're not going to find neatly trimmed lamb chops or beautifully frenched racks of lamb.
Chinese butchery is a less precise art. Here are images of what is available here in winter (lamb disappears here in the south in summer).
Lamb is often used in Mongolian style hotpot and the feet, heads and assorted bones are sold for making stocks.
Paper thin, fatty lamb rolls, 羊肉卷 (yáng ròu juǎn) are sold to be dropped into the hotpot where they cook in seconds. In many supermarkets, this is the only lamb on offer.
Elsewhere you may find 羊排 (yáng pái) which is listed in some dictionaries as 'lamb chops' but usually comes as a row (排) of undressed lamb ribs. Any additional butchery you're going to have to do yourself.
Meaty legs of lamb are available in winter. The whole legs come with skin and bone. The supermarket butchery section will chop it for you on request.
Only recently I've been able to source boneless, skinless leg meat and very good it is, too.
Despite the usual disdain for the meat, lamb skewers are popular in every evening food street and pre-assembled sticks are available laced with cubes of meat interspersed with tail fat for home grilling.
I've never been able to find my favourite cut, breast of lamb here in China 😡
Goat comes in the same cuts.
I should note that lamb is expensive here. Around double or more the price of pork. Goat is even more.