Will a Potassium atom lose or gain electrons when reacting with an iodine atom?

Iodine will grab an electron from potassium faster than you can say jack-be-nimble.  Potassium has one lone electron way outside from the rest of its electrons, and there are no secondary energy benefits to keep it (there is actually some energy benefit to losing it), so lose it is what will happen if anything comes along that has a stronger pull.  And Iodine has a much stronger pull.  Iodine is actively looking for another electron.  Potassium can barely keep that outermost one it has (give it a small kick and off that electron will fly).

In the reaction, K atom reacts to become K⁺ ion.  Hence, K atom loses one electron to become K⁺ ion.

Lose. Elements in row 1 and 2 will lose their electrons when reacting with other elements because it takes less energy to give up the 1 or 2 electron than to absorb 6 or 7 electrons.