It actually has a lot of overlap with deep learning. Here's an NLP example.
Lets say you have millions of phrases and you want to find the ones that are the most similar to a given one that you've chosen. One way of doing this would be to create embedding for each phrase and looking at some metric like cosine similarity of the embeddings to determine closeness of the phrases. The problem is, you don't want to have to compare the embedding of your phrase to every other phrase in your collection. In this case, LSH can help you narrow it down.
Lets say you have millions of phrases and you want to find the ones that are the most similar to a given one that you've chosen. One way of doing this would be to create embedding for each phrase and looking at some metric like cosine similarity of the embeddings to determine closeness of the phrases. The problem is, you don't want to have to compare the embedding of your phrase to every other phrase in your collection. In this case, LSH can help you narrow it down.