I think @Craige_Hales has the right idea in hiding the outlines that you do not want to be visible in the report. You might find it easier to do that prior to adding the report to the Dashboard - any customizations made to box properties will be remembered when the report is added to the Dashboard.
I also do not see a way to update the lambda through scripting, so I think you may need to stick with updating via the NumberEditBox. That should work even if you have hidden the display box. Here is a JSL example demonstrating this:
dt=Open("$SAMPLE_DATA/Big Class.jmp");
biv=dt<<Bivariate(
Y( :weight ),
X( :height ),
Fit Spline( 1, {Line Color( {61, 174, 70} )} )
);
Wait(1);
Report(biv)[OutlineBox(2)]<<Visibility("Collapse");
Wait(2);
Report(biv)[NumberEditBox(1)] << Set(10.0);