You will always have some residual lead in your solution - it forms as an oxide on exposure to air & becomes mixed with the sulfuric, especially on start-up. Storage of your cathode in the rinse container like lazersteve shows in his video can minimize that.
Also, I've found that some gold sponge forms on the surface of the cathode - if this is brushed off into the cell it will carry some lead with it.
I haven't found lead to be an issue, however, especially after getting some pointers from Harold. According to him, some sulfuric isn't a bad thing when going to dissolution in HCl-Cl, as lead sulfate is insoluble in it. It will appear fluffy, almost curd-like, & will filter fairly easily. As lazersteve has pointed out elsewhere, You may need to refilter solution through the same filter more than once, until the pores get sufficiently clogged to trap the finer filtrates. Your solution should be crystal clear golden yellow - if its cloudy there is still residues that should be cleaned out.
You may be experiencing other contaminates - hot sulfuric, especially if some diluted, will dissolve copper, tin, nickel. Concentrated hot sulfuric can dissolve silver. These metals would be in solution, as opposed to the gold, which is soluble only in the persulfuric (sic) acid formed directly next to the anode, it is then precipitated from the sulfuric solution that makes up the rest of the solution.
You can remove TOO MUCH lead by several boiling water rinses accompanied by stirring, allowing to settle well then siphoning.
Just my observations from my limited experiences.
Good luck!