Can a team Waive a player and then, once that player clears waivers, place them on LTIR? Or would they have to be recalled to the NHL level prior to being placed on LTIR?

To be placed on LTIR the player must be at the NHL level; however, a player CAN clear waivers, be kept at the NHL level, get injured and be placed on LTIR

Once a player clears waivers, there is no obligation to send the player to the minors, they can clear waivers and simply stay on the roster if management so chooses

LTIR use would allow the team to exceed the cap, while loaning the player to the minors would free up to a maximum of $950k in cap space

Thank you for taking an admittedly muddled question and clarifying it so well.