Once you've established a solid understanding of the entry and maintenance aspects of lapel lasso guard, you can start looking for submissions.
The triangle is an obvious first move to try for:
Similarly, the omoplata attack can be very direct, provided you can grab your partner's sleeve:
This sneaky armbar on the arm they're not really thinking about:
Or, this Kimura:
The big thing to notice is that you can control their posture with the lapel in all of these instances, augmenting fundamental submission attacks.