Suppose one learned a complete Mesechta and is just about ready to make a Siyum. Is there a time limit as to when he should make the Siyum? Can he wait 3 months to complete the last few lines?
The only sources I found on this come courtesy of chaburas.org and say one can wait a bit but not a lot.
Maharam Mintz claims that when one reaches the end of a tractate, he should delay learning the end until an appropriate time comes for making a siyum. Minchat Yitzchak (2:93) qualifies this by distinguishing between waiting a little and waiting a lot. One who finishes a tractate the week before Pesach may draw out his learning a bit so as to make a siyum on Erev Pesach, but one who finishes in December should not save the last page for the four months until he needs it to avoid having to fast. He says that in such a case, one's siyum would not be made out of simcha, but rather out of a desire to satisfy one's physical needs.
Regarding a siyum during the nine days specifically see here
However, those who complete a significant portion of learning (e.g. a tractate of Talmud) during the nine days solely for the purpose to eat meat are not universally praised. In fact, the Aruch HaShulchan, while allowing such behavior (suggesting that at least in this way, people will learn Torah) does limit the people participating in this meal to just Torah scholars associated with this learning project [Aruch HaShulchan Orech Chaim 551:28].
Nevertheless, the Mishna Berura, among others does allow broader participation in the meal, extending it to all those who would normally be invited to such a celebration [Mishna Berura 551:75]. Once the week of Tisha B'Av begins (from the Sunday before Tisha B'Av), the number of participants at such a siyum should be limited to a minyan aside from the relatives of the person making the siyum and those who are helping with them meal [Orach Chaim 551:10; Mishna Berura, ibid. note 77].