If the LS trunk is busy, then the inbound call will not even get to the Mitel phone system (or any phone system for that matter) because the busy signal is being provided by the CO, not the Mitel system.
The only way that you will be able to do any kind of voicemail is to have your LS CO trunk provider add voicemail services to your LS trunk. That means that there will be individual voicemail accounts on each LS trunk.
Now, if there is no answer on the LS trunk, then you can direct that call to the Mitel voicemail, provided that the timer in the Mitel for call forwarding is less than the timer for the voicemail account set up on each LS trunk.
Kinda silly to have 2 different voicemail accounts for each trunk if you ask me.