How does it damage proteins/lipids/DNA? There seems to be surprisingly little literature on its toxicity.
Ammonia is reportedly not toxic in bacteria even at molar conentrations (PMID 16604417).
However, yeast, plants, and animals (presumably, all eukaryotes) are unable to tolerate high intracellular ammonia concentrations. The best explanation for this phenomena I've seen is a hand-waving assertion that intracellular ammonia taxes overtaxes the cell's ability to maintain membrane gradients (PMID 7764110). However, that isn't a particularly detailed or satisfying response.
I agree with your assertion that there's a paucity of literature on the subject - we probably don't know the answer yet!
Ammonia will harm you like any other base. Although it's not directly caustic, it will cause inflammation and general "corrosion" of whatever membranes it encounters, such as those in your lungs when you get a good drag of ammonia gas. Upon contact with your body it becomes NH4OH and the hydroxide hydrolyzes amides in proteins.
Here are some articles about the neurotoxicity of ammonia.
Bosoi, C.R.; Rose, C.F. Metab Brain Dis 2009, 24, 95-102
Ammonia in solution is composed of a gas (NH3) and an ionic (NH4 +) component which are both capable of crossing plasma membranes through diffusion, channels and transport mechanisms and as a result have a direct effect on pH. Furthermore, NH4 + has similar properties as K+ and, therefore, competes with K+ on K+ transporters and channels resulting in a direct effect on membrane potential. Ammonia is also a product as well as a substrate for many different biochemical reactions and consequently, an increase in brain ammonia accompanies disturbances in cerebral metabolism. These direct effects of elevated ammonia concentrations on the brain will lead to a cascade of secondary effects and encephalopathy.
Monfort, P.; Kosenko, E.; Erceg, S.; Canales, J.-J.; Felipo, V Neurochemistry International 2002, 41, 95-102
(1) depletion of brain ATP, which, in turn, leads to release of glutamate; (2) activation of calcineurin and dephosphorylation and activation of Na+/K+-ATPase in brain, thus increasing ATP consumption; (3) impairment of mitochondrial function and calcium homeostasis at different levels, thus decreasing ATP synthesis; (4) activation of calpain that degrades the microtubule-associated protein MAP-2, thus altering the microtubular network; (5) increased formation of nitric oxide (NO) formation, which, in turn, reduces the activity of glutamine synthetase, thus reducing the elimination of ammonia in brain.
Skowrońska, M.; Albrecht, J. Neurochemistry International 2013, 65, 731-737
An increase of brain ammonia in experimental animals or treatment of cultured astrocytes with ammonia generates reactive oxygen and nitrogen species in the target tissues, leading to oxidative/nitrosative stress (ONS). In cultured astrocytes, ammonia-induced ONS is invariably associated with the increase of the astrocytic cell volume. Interrelated mechanisms underlying this response include increased nitric oxide (NO) synthesis which is partly coupled to the activation of NMDA receptors and increased generation of reactive oxygen species by NADPH oxidase. ONS and astrocytic swelling are further augmented by excessive synthesis of glutamine (Gln) which impairs mitochondrial function following its accumulation in there and degradation back to ammonia (“the Trojan horse” hypothesis). Ammonia also induces ONS in other cell types of the CNS: neurons, microglia and the brain capillary endothelial cells (BCEC). ONS in microglia contributes to the central inflammatory response, while its metabolic and pathophysiological consequences in the BCEC evolve to the vasogenic brain edema associated with HE. Ammonia-induced ONS results in the oxidation of mRNA and nitration/nitrosylation of proteins which impact intracellular metabolism and potentiate the neurotoxic effects.