SOIR covers players who didn't play any games last year, and they don't count against the Cap. Here is a piece from the CBA that addresses it.
What is the season opening injured reserve (SOIR)?
If a player is injured during training-camp, they can be placed on season-opening injured reserve, to possibly obtain cap relief. It is notable that the SOIR equations are not the same as the daily rate equations in CBA 15.6, which is instead used to calculate the players daily salary (as opposed to cap hit).
Full Cap Hit
Players who are on a one-way contract, or players on a two-way contract who accrued 50 or more NHL games in the previous season count fully against the cap hit. Teams can opt to place these players on LTIR to obtain cap-relief (LTIR FAQ).
Discounted Cap Hit
Players on a two-way contract, who accrued 1-49 NHL games in the previous season, count against the teams cap hit; however, the reduced cap hit is calculated as follows:
Multiply the players NHL cap hit by the total accrued NHL days in the previous season, and divide by the total number of days in the previous season (Ex: 186 for 2014-15)
When a player is reactivated to the active roster, their cap hit reverts back to the full rate
Full cap relief
Players who did not accrue any NHL games in the previous season, can be placed on SOIR and do not count against their teams cap hit.
Toronto doesn't have to get under the cap for day 1 of the regular season. Teams can use the LTIR exception on the final day of training camp instead of waiting till the start of the regular season, however the amount of cap relief gained differs based on which option they choose.
Teams are usually better off being compliant on day 1, but I don't think it matters for Toronto unless they do something crazy to add a lot more salary. They can LTIR one of Lupul/Horton on the last day of training camp, then LTIR the other whenever necessary during the regular season and be fine with their current roster and re-signing Brown.
That's not quite accurate how LTIR works. They do count, it's the mechanics of how and when the LTIR exceptions are exercised that determine how much they count against the cap. It's almost never 100% relief in practice.