The NHL set dates for offseason in the new CBA with tentative timelines based on when the NHL season might actually end. They had to adjust it at the last minute when the CBA negotiations took longer than expected, but the original tentative date for the 2020 NHL Entry Draft was listed as October 6 in the final version of the CBA Memo of Understanding released in July. Unfortunately, at the time of the second draft lottery, the NHL announced the dates at October 9 and 10.
Today the original date has been confirmed with round one taking place on Tuesday, October 6 and the rest of the draft the next day. There is no chance now that the Stanley Cup Final will run past October 2, so the date can be confirmed.
The last possible date for a Conference Final game is September 19, 2020, leaving time to play the final round, potentially, before the end of September.
The NHL draft is usually on a Friday and Saturday in June. No details have been released yet on the form of the draft event. Originally scheduled to take place in Montréal, there will be no live presentation.