Input method editor (IME) converts sequential alphabet key inputs to words in a target language. It is an indispensable service for billions of Asian users. Although the neural-based language model is extensively studied and shows promising results in sequence-to-sequence tasks, applying a neural-based language model to IME was not considered feasible due to high latency when converting words on user devices. In this work, we articulate the bottleneck of neural IME decoding to be the heavy softmax computation over a large vocabulary. We propose an approach that incrementally builds a subset vocabulary from the word lattice. Our approach always computes the probability with a selected subset vocabulary. When the selected vocabulary is updated, the stale probabilities in previous steps are fixed by recomputing the missing logits. The experiments on Japanese IME benchmark shows an over 50x speedup for the softmax computations comparing to the baseline, reaching real-time speed even on commodity CPU without losing conversion accuracy. The approach is potentially applicable to other incremental sequence-to-sequence decoding tasks such as real-time continuous speech recognition.