These two are clearly distinguished by their endings, but they are still often confused.
Both come from the Latin verb laudare, ‘to praise’. Laudable means ‘deserving praise, praiseworthy’: a laudable attempt in the competition. Laudatory means ‘giving praise’: a laudatory speech about the prizewinner. The pronunciation of both is /lawd-/, not /lowd-/.
In some contexts, laudable is a rather unenthusiastic description, ‘damning with faint praise’, because of its formal tone: His attempt was laudable but misguided.
Laud as both noun and verb, meaning ‘praise’ or ‘to praise’, is now even rarer than laudable and laudatory. As a verb, it occurs most often in the expression lauded to the skies. As a noun, it can still be found in hymns:
All laud we would render: O help us to see ‘Tis only the splendour of light hideth Thee.
-Hymn: ‘Immortal, invisible, God only wise’, Hymns Ancient and Modern