Maybe lsim is not the right function to use. I solved the problem by using sim instead, which has options including to add noise:
opt = simOptions('AddNoise',true);
y = sim(sys,u,opt);
I didn't know about sim. According to the documentation, the differences between the two functions are:
y = sim(sys,udata) returns the simulated response of an identified model using the input data, udata.
y = lsim(sys,u,t) simulates the (time) response of continuous or discrete linear systems to arbitrary inputs.
Not sure I understand the differences...