Found my answer ! To access the properties of the ltiblock (in my example it is a ltiblock.gain), as maximum and minimum reachable values, you have to create an ltiblock parameterized as you need and then use the setBlockParam function. This could be done like this for my example :
st0 = slTunable('model','K'); % Definition of the interface between Simulink and Matlab for Systune
K_wanted = ltiblock.gain('K',Ny,Nu); % Def of a tunable gain with Ny outputs and Nu inputs
K_wanted.Gain.Maximum = K_max;
K_wanted.Gain.Minimum = K_min;
st0.setBlockParam('K',K_wanted);
This last lign changes the default parameterization of K into the parameterization defined by the ltiblock.gain K_wanted which contains the bounds. We can verify that with :
st0.getBlockParam('K').Gain.Maximum
% or
st1.getBlockParam('K').Gain.Minimum
It is not really a straightforward solution but at least it works !