The current system handles punishments in 4 tiers:
1.) 10 game chat restriction
2.) 25 game chat restriction
3.) 14 day ban
4.) Permanent ban
You start at tier 1 for your first punishment, and each punishment after that moves you up to the next tier, regardless of how minor the offense was. However, it is possible to skip tiers if Riot deems your behavior severe enough. This is generally done with things like death threats, racist/homophobic slurs, telling others to commit suicide, etc.
You had already gone through the 2 sets of chat restrictions, so normally your next punishment (this one) would be a 14 day ban. However, telling someone to kill themselves is definitely worthy of an escalation. That kind of behavior is not tolerated at all.