For alkali and lanthanide metals, is there a better liquid barrier to oxidation than mineral oil? Most often mineral oil is used to store, protect reactive metals from oxidation. By far the best choice is to hermetically seal the metal in pure argon or some other inert gas, since, although mineral oil tends to slow down the oxidation process, it's still soluble to oxygen and slowly but surely the metal will begin to oxidize.

While argon is a sure thing it requires special equipment, and once sealed you have to break the container to access the metal.

My question - among liquids is there a better choice than mineral oil? A liquid that will not react with the metals, and provide a better barrier to migration of oxygen?
Not really as all liquids will, to some extent, dissolve a small amount of oxygen or water. The only liquid that comes to mind that will prevent either is mercury, but you probably don't want your stuff contaminated with mercury. If you really wanted to prevent water contamination, adding molecular sieves might help, but other than that, no not really.