Filtering home-rendered lard
For applications such as these where I really want a fine strain, much more than any of my strainers can handle, I line a larger-hole strainer with cheesecloth (if I have trouble with the cheesecloth staying I use a rubber band to hold it in place).

Although I have not tried it with rendered lard, I have used it in a lot of other places (stock immediately comes to mind) where I have a lot of little particles that make it through my finest of strainers.  A quick search for a lard/cheesecloth/strainer keyword combination shows that a lot of recipes for home-rendered lard seem to suggest this so I think it would work.

You can find a picture of a cheesecloth-lined strainer here or just Google image search it if the link dies.

Oh, and as an aside, I find that purchasing the cheesecloth in bulk at a fabric store (such as Jo-Ann Fabrics in the USA) is much, much cheaper than buying small packages in a kitchen store (such as Williams-Sonoma).