"Ongoing" or "on-going"

Solution 1:

Either is acceptable, though the form ongoing is almost uniquely the one used in modern times. (The hyphenated version, as with most compound words in English, was the original form; the hyphen got dropped after time as the word became more common.)as

The Online Etymology Dictionary gives the following origin:

ongoing
also on-going, 1877, from on + going (see go).

Solution 2:

This link provides some guidance. To quote:

This word never has been hyphenated, but people think that it is a mix of ‘on’ and ‘going’, but if you think of someone ‘going on about grammar’, you would not say that that person was ‘ongoing’!