What is the geometrical structure of Pb3O4? I'm confused by the structure of Pb3O4. There are some sites claiming that it is a six membered ring of alternating Lead and Oxygen atoms with another Oxygen atom in the center bonding with 2 out of the 3 Lead atoms. 

There are other sources which claim that it is actually two 4 membered rings of alternating lead and oxygen atoms with a lead atom in common between the 2 rings.

Moreover, isn't Lead a metal? Then How can it combine with oxygen in such "bonds" whereas ionic bonds are non-directional?
Maybe below 3d structure of Pb3O4 will help?

3d structure of Pb3O4

Also in the below link of a pdf, just before the discussion section the paragraph clearly states that there are both ionic and covalent bonds present in Pb3O4.

REsearch Paper on Pb3O4 structure

Thus we can conclude that it is Tetragonal, tP28 .(as per the link provided by Maxw in the comment to your question)

Also metals can form covalent bonds. Refer to below question and its answers:
Metals forming covalent bonds