Create handles for each plot call, and then use the first elements of those handles as the first argument to legend —
t = linspace(0, 2*pi);
z1grid = (1:5).'*sin(t);
z2grid = (1:5).'*sin(2*t) + 5;
z3grid = (1:5).'*sin(3*t) + 10;
z4grid = (1:5).'*sin(4*t) + 15;
figure
hold on
hp1 = plot(t,z1grid,'color','red','DisplayName','lower');
hp2 = plot(t,z2grid,'color','yellow','DisplayName','lowermid');
hp3 = plot(t,z3grid,'color','green','DisplayName','uppermid');
hp4 = plot(t,z4grid,'color','blue','DisplayName','upper');
hold off
legend([hp1(1) hp2(1) hp3(1) hp4(1)], 'Location','best')
.
