I see that Cisco LAP 1240 support Mesh mode, but I am not sure if LAP 1250 support or not? I can't find any document that say about this.
Depends on the WLC software that you are using!! if you are running the latest 7.0.116 then the Indoor mesh is supported using 1250 series APs..
With the 188.8.131.52 release, the mesh functionality is added in the Cisco Aironet 1040, 1140, 1250, 1260, 1520, and 3500 series indoor access points. The mesh backhaul radio supports the 802.11n data rate. When operating in mesh mode, their mesh backhaul will support both the 802.11a and 802.11n data rate.
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