Is it permissible/ideal to eat food with a Lubavitch Hechsher cooked in Keilim that were used to cook food without a Lubavitch Hechsher?
Lubavitch meat cooked in Keilim or in an oven which were used to cook non-Lubavitch meat but with a good hechsher?
How about Parve food (such as fish, eggs, bread, pastry) cooked in Fleishig oven or Keilim?
Regarding Milchig, I understand that it is not permitted to eat Cholov Yisroel foods that were cooked with Keilim used for non Cholov Yisroel.
If the food is 100% kosher, you may eat the food too, needless to say that it is permitted to eat food cooked in such utensils.
One may eat non-Lubavitch meat.
Obviously, the same answer applies to Parve food cooked in meat utensils.
Your understating regarding cooking Milchigs in non Cholov Yisroel Keilim is correct. However, if 24 hours have passed since it was used for non Cholov Yisroel and the Keilim were clean and the food was already cooked, not by your request, the food may then be eaten.
There is no difference between Keilim and an oven.