If you have say... 10K miles on the loaner... .and you do a 36K mile lease, then the tires will have 46K miles by the end of the lease, and will be more likely to fail turn-in inspection....
Other than that, if the total lease cost is less than new, there really is no downside, assuming you are under warranty/maintenance for the entire term (as noted above, check the in-service date).
2006 330Ci ZHP Imola Red
2011 X3 Bluewater
1987 325iS Bronzit (retired)
2011 Z4 Space Gray (retired)
2008 X3 Sapphire Black (retired)
2005 330Cic Silver-Gray (retired)
2003 325i Sport Steel Blue (retired)
1967 2000CS Delphin Gray (retired)