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LambdaRank has no loss function. Explain how you train...
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See plansLead with what gradient descent actually requires - a vector to add to the parameters, not a scalar to minimize - then show the chain rule doing the work: you specify the gradient of the cost with respect to the score by hand, the gradient of the score with respect to parameters comes from ordinary backpropagation, and the gradient of the cost with respect to parameters is computable without the cost function ever existing. Be honest about the cost: no loss means no convergence guarantee and no comparable number across runs, which is why held-out NDCG is the only stopping criterion available.