What metabolite intermediate will accumulate in a mammalian cell-free extracts capable of glycolysis if lactate dehydrogenase is inhibited?
As you probably know, lactate dehydrogenase catalyzes the interconversion of pyruvate and lactate, with electron transfer via NADH/NAD⁺. If lactate dehydrogenase is inhibited, the fate of pyruvate in the cell extract will depend on what cell structures as wells as enzymes and other compounds are available. In other words, the answer to your question will likely be strongly dependent on the organism, as well as the particular circumstances of the experiment you are performing. 

To give you a speculative answer: Assuming that the metabolic pathways of the mammalian cell still function and that oxygen is available to accept electrons in respiration, pyruvate could be metabolized through the tricarboxylic acid cycle, forming energy-rich compounds and carbon dioxide. If other fermentative pathways are available, pyruvate could be funnelled into those.

In any case, predicting what compunds would accumulate would require more information than that which is given in your question.