[abridged] We present 52-93 micron spectra obtained with Spitzer in the MIPS-SED mode, of a representative sample of luminous compact far-IR sources in the LMC. These include carbon stars, OH/IR AGB stars, post-AGB objects and PNe, RCrB-type star HV2671, OH/IR red supergiants WOHG064 and IRAS05280-6910, B[e] stars IRAS04530-6916, R66 and R126, Wolf-Rayet star Brey3a, Luminous Blue Variable R71, supernova remnant N49, a large number of young stellar objects, compact HII regions and molecular cores, and a background galaxy (z~0.175). We use the spectra to constrain the presence and temperature of cold dust and the excitation conditions and shocks within the neutral and ionized gas, in the circumstellar environments and interfaces with the surrounding ISM. Evolved stars, including LBV R71, lack cold dust except in some cases where we argue that this is swept-up ISM. This leads to an estimate of the duration of the prolific dust-producing phase (superwind) of several thousand years for both RSGs and massive AGB stars, with a similar fractional mass loss experienced despite the different masses. We tentatively detect line emission from neutral oxygen in the extreme RSG WOHG064, with implications for the wind driving. In N49, the shock between the supernova ejecta and ISM is revealed by its strong [OI] 63-micron emission and possibly water vapour; we estimate that 0.2 Msun of ISM dust was swept up. Some of the compact HII regions display pronounced [OIII] 88-micron emission. The efficiency of photo-electric heating in the interfaces of ionized gas and molecular clouds is estimated at 0.1-0.3%. We confirm earlier indications of a low nitrogen content in the LMC. Evidence for solid state emission features is found in both young and evolved object; some of the YSOs are found to contain crystalline water ice.
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