For most IRC users there are two chat clusters you need to be concerned with: main and event. You can access a particular channel from any server within a cluster to which it is assigned. Almost all channels will be on the main cluster with the exception of extremely large channels (riotgames) or events (esports, E3, TwitchCon, etc.).
There are various API endpoints you can use to determine which cluster a channel resides on including the one you mentioned above. For example:
Main: http://tmi.twitch.tv/servers?channel=lirik
Event: http://tmi.twitch.tv/servers?channel=riotgames
The cluster value will tell you which you need to connect to and the servers array will give you a list of IRC compatible servers. (Note: you can also use port 6667)
How many connections you uses depends on how active the channels and bot is. If they are a few smaller channels you can probably group them on a single connection. If you are receiving too many messages on a single connection you might reach the limit of the server’s sending buffer and get disconnected.