Most newer Cisco AP's can now be ordered in either Autonomous or LWAPP configurations and the 1250 Series is no exception :) You are most correct that if using the Lightweight/Unified Wireless deployment ordering the LAP (Lightweight Model) of a specific AP makes the setup much simpler. Here is the related 1250 info;
Cisco Aironet 1250 Series with Pre-installed Radio Modules
Here is the Autonomous (Stand-Alone) model;
AIR-AP1252AG-x-K9 (802.11a/g/n-d2.0 2.4/5-GHz Mod Auto AP; 6 RP-TNC)
Here is the LWAPP model;
AIR-LAP1252AG-x-K9 (802.11a/g/n-d2.0 2.4/5-GHz Mod Unified AP; 6 RP-TNC)
**Note that in contrast to previous models of Cisco Aironet access points, an external AC power supply and power cord does not ship standard with Cisco Aironet 1250 Series Access Point. An optional external AC power supply is available, but is required only if AC power will be used to power the access point. The external AC power supply is not needed if the AIR-PWRINJ4 power injector is used to power the access point; the injector has its own integrated AC power supply.