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
1995 M3 Montreal Blue
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)