Lesquels & Lesquelles and Quels

Quel...etc is an interrogative adjective and needs a noun: quelles chaussures?  -- what shoes?

Lequel...etc. has several different uses. It can be an interrogative pronoun, a relative pronoun and even a relative adjective. If we concentrate on its use as an interrogative pronoun, the difference to quel is that it refers to something already mentioned previously. It also implies a limited selection to choose from, whereas quel  leaves the field wide open.

Tu as quelles chaussures? -- What shoes do you have?
J'ai beaucoup de chaussures. Lesquelles? -- I have many shoes. Which ones?