Seems adding the #lname template ref is the problem.
<input [(ngModel)]="ng2Form.lname"
name="lname" id="lname"
type="text"
#lname="ngModel"
required
placeholder="Last name" />
...otherwise, the form works as expected.
Plunk: read the errors in the console. Console error message:
There is no directive with "exportAs" set to "ngModel"
[ERROR ->]#lname="ngModel"
Looks to be the same issue reported here:
https://github.com/angular/angular/issues/9363