Learn French: Le lavabo sur lequel tu poses le savon est petit. - The washbasin on which you put the soap is small.

Lequel translates to "which" and is used here after the preposition sur (on) to refer back to le lavabo (the washbasin). Because le lavabo is masculine and singular, we use the matching masculine singular form, lequel.

Could I just say sur que or sur qui instead of sur lequel?

No. In French, you cannot use que after a preposition. You can use qui after a preposition (like sur qui or avec qui), but only when referring to a person! Since a washbasin is a thing, you must use a form of lequel after prepositions like sur, avec, or pour.

Why use poses instead of mets for "put"?

While mettre is the general word for "to put", poser specifically means to "set down" or "place" something on a surface. Since you are setting the soap down on the sink, poser is a very natural verb to use here.

Why is est petit all the way at the end of the sentence?

The core of the sentence is simply Le lavabo est petit (The washbasin is small). The extra descriptive phrase sur lequel tu poses le savon (on which you put the soap) gets inserted right after the noun it describes, temporarily interrupting the main idea.