What does "Ach" come to preclude?
Rashi: It comes to preclude Yehoshua and Calev, who were given their portion in Eretz Yisrael without lots. 1
Seforno: Even though the portions were divided up according to size, 2 the division was made exclusively by means of lots.
How was the Goral actually carried out?
Rashi (on Pasuk 54, citing Bava Basra, 122a): 'Elazar the Kohen Gadol, who was wearing the Urim ve'Tumim, announced with Ru'ach ha'Kodesh "In the event that Sheivet P'loni emerges, the following borders will emerge together with it!" The names of the tribes were written on twelve slips, and the twelve areas of Eretz Yisrael on twelve slips. He would then mix the slips in a box and the prince of the named tribe would place his hand inside the box and draw two slips
Rashi: 'Finally, based on the Pasuk later (Pasuk 56), "Al-pi ha'Goral", the lot would announce "I, the lot of G'vul P'loni, emerged for Sheivet P'loni!" '
What are the connotations of "li'Shemos Matos Avosam Yinchyalu"?
Rashi #1 and Ramban: Having insinuated earlier 1 that the land was to be distributed according to those who were about to enter Eretz Yisrael and who were being counted now, the Torah is now teaching us that, unlike all other cases of inheritance in the Torah, the inheritance here first went back to those who left Egypt 2 who had already died, and the living now inherited the deceased (from the grave). 3
Rashi #2: It automatically precludes Geirim and Avadim from receiving a portion.
In Pasuk 53. See Sifsei Chachamim.
Rashi learns this from the word "Matos", the Ramban, from the word "Avosam," since 'Matos' is synonymous with 'Sheivet', meaning 'tribe', as we find frequently (See Ramban).
Rashi: Consequently, if two brothers left Egypt, one leaving one son who entered Eretz Yisrael, the other one three sons, the former received one portion, the latter, three. The four portions then went back to their deceased father, two of which he bequeathed to the one son, and two, to the three sons.