Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
There is no sin in buying common land since selling such land is permissible and isn`t considered aleatory. It is mentioned in {Tabyeen al-Haqaa`iq}, "It is permissible to sell common land, dividable or not." It is also stated in {Al-Majmou` Shareh al-Mohathib}, "Common property is permissible to sell."
Moreover, there is no sin in drawing lots to determine the share of every partner because this one method of division. It is stated in the Maliki book {Al-Shareh al-Kabeer LilSheikh Ad-Dardeer},"There are three ways of dividing land; one of them is by drawing lots to determine the share of each partner….." Kindly check the Hanafi book {Ad-Dor Al-Mokhtar}.
Ibn Hajar stated, "Scholars have disagreed on the validity of drawing lots, however, the majority approved it while some Hanafi scholars didn`t. In addition, Ibn al-Monther reported that Abu Hanifah approved it. Actually, drawing lots is resorted to in case there is a dispute amongst partners, by they two or more…" {Fateh al-Bari}. For more information, kindly check {Rawdat at-Talibeen, V.11:204}. And Allah the Almighty knows best.