Just adding one more hint to the above instructions: Always tune your strings without any levers engaged. (You may already be doing this - if so, disregard my reminder).
The reason is, the lever may possibly restrict the stretching of the string, so when you tighten the tuning peg the string responds more slowly to the changes. You think it's in tune, then later the string slips a bit more past the lever & you're out of tune again.
Also, with some levers, you can cause excessive wear on the string by tuning while the lever is engaged.
Can you describe what sort of lever you have? Or do you know the brand of the harp? It could be worthwhile to consult with the harp- or lever- maker to see if there are any hints beyond the general info presented already.
The common lever styles/brands in America are "blades" (flat piece mounted to one side of the string that rotates to press the string), Robinson (a black plastic lever presses the string toward the neck, pinching it against a pin), Loveland or Jordan (lever is mounted between the neck & the string, & "lifts up" against the string. Loveland are gold plated, Jordan are plastic), or Camac (lever lifts up but moves a fret against the side of the string rather than pressing toward or away from the neck). Blades can be tough to adjust. The others should be able to be moved at least a little without having to re-drill any holes.
Note: some relatively inexpensive "Celtic" harps that are sold through various retail/catalog outlets are imported from Pakistan (usually via Mid-East Manufacturing). They look lovely, with carved rosewood sides etc. but quality control is sometimes questionable. Some of these "harp-shaped-objects" are virtually unplayable as musical instruments, others require significant surgery - including replacing strings & levers - to make them at best mediocre. Some fall apart quickly once you brin the strings up to standard tension. On the other hand, sometimes you get an instrument that is halfway decent - but it's a gamble. I don't know if any of that applies to your particular instrument, just throwing out some info.
(amateur harp builder as well as player)