Acids for dishwasher or washing machine cleaning
Are meant to deal with hard mineral deposits and powdered detergent residue along with perhaps scum created when alkaline substances are in contact with alkaline substances. They do not per se deal with "lard", grease or oil residue.
For dealing with oils or fats you are actually going to want something that is base/alkaline pH. If you are worried about any waxy or whatever coating inside your washer from the liquid detergent, just start using any good powdered product. After several washes things should be fine.
OTOH if you still want to go the acid route I'd look for a dishwasher/washing machine cleaner. They are usually combinations of acids and surfactants designed to deal with a wider range of residues/substances than just mineral deposits.
Failing this there is the old standby of baking soda and acid (vinegar or citric). Has been years since have done it so cannot recall the ratio but you can "Google" for more information.
The idea is that when the base and acid meet the chemical reaction causes a frothing which does most of the cleaning.