Hello Borichouch73
Firstly, welcome to the SBB Community!
Holding the Saver Day Pass, it is not possible to reserve seats on a direct train from Lucerne or Arth-Goldau to Milan.
What you could do, i. addition to your SDP, you could purchase a Trenitalia Eurocity Ticket Chiasso-Milan, which comes with a complimentary seat reservation, and then, after boarding in Lucerne / Arth-Goldau, see if the allocated seats are unoccupied from your boarding station already. If yes, fine, if not, you would have to change coaches / seats in Chiasso to take your reserved seats.
However, most people having the Saver Day Pass do not use the Eurocity at all as they travel with the IC2 to Lugano and continue on the RE80 from there using an Arcobaleno Transfrontaliera ticket Chiasso-Milan, while the SDP covers the portion to the border. No seat reservation is needed.
Kind regards,
Roland