How does the Evangelical Lutheran Church in America handle heresies? As far as I know, I am aware, from a simple Google search, that the Evangelical Lutheran Church in America, the largest Lutheran denomination in the United States, considers the twofold rule of God theology a heresy - or at least a misuse of it. Okay. In such a case, or another case in which a person (layperson or clergy) wilfully follows unorthodox beliefs and practices, how does the ELCA deal with them?

I am aware that individual Lutheran congregations are governed by synods. So, what does synod say?
The guideline for discipline of clergy can be found here:
http://download.elca.org/ELCA%20Resource%20Repository/Discipline_Process.pdf

The above disciplinary process is intended for rostered leaders, including associates in ministry, ordained clergy, diaconal ministers, deaconesses, etc.  Considering the complexity of the twofold rule of God theology, it is unlikely that error on this matter alone would be treated harshly.  Disciplinary action is more likely to occur should the theological error becomes manifest in some form of behavior or activity that is in contradiction with accepted witness of the Gospel and the ELCA Visions and Expectations for rostered leaders.  The guidelines known as Visions and Expectations are slightly different depending on the type of rostered leader.  These guidelines can be found here:
http://www.elca.org/en/About/Churchwide/Office-of-the-Secretary/Rostered-Leaders

Because American culture is currently undergoing massive social change in the wake of the advent of global interconnectedness through technology and business, and because the ELCA is in the midst of the development of ecumenical and interreligious relationships, the theological error wherein the unmerited grace of God is put forth as the governing principle of human society is more likely to occur and less likely to raise alarm among the leadership of the ELCA. This error supplants the rule of law with the gospel resulting in a theology of "cheap grace" wherein there is neither need nor demand for discipleship. Amidst the important and worthy need and effort to become radically inclusive and courageously cooperative, we are tempted to preach God's rule of law weakly, particularly on matters where we find ourselves in disagreement with those with who we seek to be in close partnership, whether religious, political or social allies.  American Lutherans seem to try really hard to be nice and avoid public controversy and conflict.
Errors that are more likely to initiate disciplinary action are those that indicate that adherence to a particular legal or moral code are redemptive and necessary for one's salvation and/or participation in the community of faith.  This is error that supplants God's rule of grace in the community of Christ and negates the redemptive action of Christ (a heresy colloquially known as "works righteousness" or "salvation by works").  While Lutherans are no less likely to engage in this kind of heresy, we are very sensitive about it because our theological and reformation heritage is rooted in the doctrine of salvation "by grace alone through faith alone."  

It is unlikely that theological error on this matter would result in discipline for heresy for a layperson (unless perhaps, that layperson served their congregation in the ministry of Word and was deliberately teaching in contradiction to the ELCA teaching).  Because of the complexity and semi-paradoxical nature of twofold rule theology, error on the part of a layperson could be resolved with education rather than discipline.