If you remove the zeros then your kx and ky will have less values and if you omit the x-values when calling plot by default it sets them to 1:numel(y-values). Therefore, say you have 12 values after removing the zeros it will plot kx from 1 to 12.
What you have to do is find at which positions your non-zero values are and call plot(X,Y).
Another remark, since you know how many iterations you'll have to do in the loop, call explicitly for.
mfp = 31; % mean free path (nm)
k = 316.72; % conductivity (W / m*k)
% Preallocate kx and ky (search for preallocation for details)
kx = zeros(Lmax,1);
ky = zeros(Lmax,1);
% Loop from 30 to 140 with a step of 10.
for ii = 30:10:140
kx(ii) = k*(1-(2*mfp/(3*3.14*ii)));
ky(ii) = k*(1-(mfp/(3*ii)));
end
% Find the positions (x coordinates) of the non zero entries in kx
idx = find(kx);
plot(idx,kx(idx),'-')
hold on
% Find the positions (x coordinates) of the non zero entries in ky
idx = find(ky);
plot(idx,ky(idx),'--')
plot([30,140],[316.72,316.72]);
grid on
EDIT
A vectorized alternative:
mfp = 31; % mean free path (nm)
k = 316.72; % conductivity (W / m*k)
L = 30:10:140;
kx = k*(1-(2*mfp./(3*3.14*L)));
ky = k*(1-(mfp./(3*L)));
x = 1:numel(L);
plot(x,kx,'-',x,ky,'--',[x(1) x(end)],[316.72,316.72])
set(gca,'Xlim',[x(1) x(end)],'XtickLabel',L)
