I'm not 100% sure I understood your question. If I understood correctly, you still want 7 lines, with 7 different colors (so the plot itself won't change), but instead of a legend you want a colorbar.
The first thing I think you will need to change to get that working is the colors. The default 7 colors come from the axes ColorOrder, and are not part of a colormap. In fact, they are 7 colors picked to be distinct from one another, instead of part of a gradient.
colors = parula(7);
Now you can plot your 7 lines, and specify your 7 colors. Note: It is up to you to make sure lines are colored in the correct order based on the data and ticks you select later.
madeupdata = magic(7);
p = loglog(madeupdata);
for ii = 1:7
p(ii).Color = colors(ii,:);
end
% set(p,{'Color'},mat2cell(colors,ones(1,7))) % Same as for loop above.
Once that is done, you need to create a colorbar with the same colormap, and manually set the ticks:
set(gca,'CLim',[-3 3]);
c = colorbar;
c.Colormap = parula;
c.Limits = [-3 3];
c.Ticks = -3:3;
Does that get you close to what you are trying to do?
