There seems to be two possible approaches when it comes to mixing iodine with lipid. In one version, you can mix it with unsaturated lipids, such as vegetable oils. In another version, you can mix it with saturated lipids, such as mineral oil. Both versions have their proponents with different reason why one version is better than the other, but without proper experiments we cannot know what is the best approach.
Here is the first version:
And the second version, which also has a recipe:
Here is the first version:
US20030026852A1 - Molecular iodine pharmaceutical composition - Google Patents
This invention describes a non-aqueous oral composition of molecular iodine in a stabilized hydrophobic environment containing a hydrophobe or combination of hydrophobes for treating different disease states.
patents.google.com
And the second version, which also has a recipe:
US4012504A - Iodine mineral oil solution for preventing bovine mastitis - Google Patents
A solution of iodine in mineral oil is externally applied to cow teats to control the spread of bovine mastitis and to heal chapping and chafing. The composition is made by agitating elemental iodine in heated mineral oil until it dissolves. An improved teat dip includes, in addition to the...
patents.google.com