Let's say that the 120 days work permit is approved by authorities but a project requires the person to continue after 120 days, as well without any gap. So in that case, is it really mandatory to have 2 months cooling off period for the 120 days permit to be followed by a L permit?
A 120-day L permit is designed to allow up to 120 days of work in Switzerland in any 12-month period. It is for short-term workers exempt from the quota.
You cannot obtain another 120-day permit if you have already used up 120 days in the previous 12-month period. Some cantons may be more lenient if there is actual exceptional circumstances or particularities, but you can't count on it.
You may obtain another short-term permit (usually less than 4 months) after a two-month cooling off period.
You can also obtain without a gap a year-long L permit, but that will be subject to the quota.