Many people, maybe even most, who take Lasix take a prescription potassium supplement on a daily basis. Our bodies are pretty adept at eliminating extra potassium so unless there is something that really interfers (such as kidney problems) we rarely go dangeriously high.
On the reverse, low potassium levels are very very common with anyone on a diuretic and cause not only achiness, joint and muscle pain, constipation, and fatigue but also life threatening heart rhythms.
I'm on moduretic (a potassium sparing diuretic), lasix, and K-dur(a potassium supplement). I don't routinely have my potassium checked unless something else is being done.
Before I was on lasix I took K-dur three times a week otherwise my potassium would drop. When I had lasix added I had my potassium increased to daily. I am not on an ace inhibitor but it sounds like that could be a problem