Designing a Low-Level Design (LLD) for a distributed search engine using machine coding would involve several steps and considerations. Here are some of the key features and requirements that should be considered:

1. Indexing: The search engine should be able to index a large number of documents quickly and efficiently. This could be accomplished using a data structure like inverted index or trie.

2. Query Processing: The search engine should be able to handle a large number of queries and return relevant results quickly and accurately. This could be accomplished using search algorithms like Boolean search, Vector Space Model, BM25.

3. Distributed Architecture: The search engine should be designed as a distributed system, with multiple servers working together to handle queries and index documents.

4. Fault-tolerance: The search engine should be able to handle server failures and still be able to provide search results. This could be accomplished by having multiple replica of the same data on different servers, and a failover mechanism to redirect traffic to available servers.

5. Scalability: The search engine should be designed to handle a large number of queries and be able to scale horizontally by adding more servers as needed.

6. Security: The search engine should be designed to protect user data and ensure the security of the data stored in the system.

7. Monitoring: The system should be equipped with monitoring and logging capabilities, allowing system administrators to track usage, performance, and identify any issues that may arise.

8. Analytics: The system should provide analytical capabilities to understand the behavior of users and the effectiveness of the search algorithm.

9. User Interface: A user-friendly interface should be provided to users to query the search engine.

10. Caching: A caching mechanism could be implemented to speed up the search results for frequently queried data.

This is a general list of features and requirements that should be considered when designing a distributed search engine. In a real-world scenario, additional requirements may be identified and incorporated into the design.

Here is an example of how the classes might be organized:

1. Document class - This class would represent a document in the search engine. It would have properties such as the document's unique identifier, and a key-value map of the fields and values in the document.

2. Index class - This class would represent an index of documents. It would have properties such as a list of documents and a data structure (e.g. inverted index) to store the mappings of words to the documents they appear in.

3. Node class - This class would represent a node in the distributed search engine. Each node would have its own index and would be responsible for handling search requests for its subset of the documents.

4. Cluster class - This class would represent the cluster of nodes in the distributed search engine. It would have properties such as a list of nodes and methods for managing the distribution of documents among the nodes and handling search requests.

5. SearchEngine class - This class would represent the search engine itself. It would have properties such as the cluster of nodes and methods for handling search requests and returning the results.

Here is an example of how the classes might be implemented:

public class Document {
    private String id;
    private Map<String, Object> fields;

    public Document(String id) {
        this.id = id;
        this.fields = new HashMap<>();
    }

    public String getId() {
        return id;
    }

    public Map<String, Object> getFields() {
        return fields;
    }

    public void addField(String key, Object value) {
        fields.put(key, value);
    }

    public Object getField(String key) {
        return fields.get(key);
    }
}

public class Index {
    private Map<String, Set<Document>> invertedIndex;

    public Index() {
        this.invertedIndex = new HashMap<>();
    }

    public void addDocument(Document document) {
        for (Map.Entry<String, Object> field : document.getFields().entrySet()) {
            String fieldValue = field.getValue().toString();
            for (String word : fieldValue.split(" ")) {
                if (!invertedIndex.containsKey(word)) {
                    invertedIndex.put(word, new HashSet<>());
                }
                invertedIndex.get(word).add(document);
            }
        }
    }

    public Set<Document> search(String query) {
        Set<Document> result = new HashSet<>();
        for (String word : query.split(" ")) {
            if (invertedIndex.containsKey(word)) {
                result.addAll(invertedIndex.get(word));
            }
        }
        return result;
    }
}

public class Node {
    private String hostname;
    private Index index;

    public Node(String hostname) {
        this.hostname = hostname;
        this.index = new Index();
    }

    public String getHostname() {
        return hostname;
    }

    public Index getIndex() {
        return index;
    }

    public void addDocument(Document document) {
        index.addDocument(document);
    }

    public Set<Document> search(String query) {
        return index.search(query);
    }
}

public class Cluster {
    private List<Node> nodes;

    public Cluster(List<Node> nodes) {
        this.nodes = nodes;
    }

    public List<Node> getNodes() {
        return nodes;
    }

    public void addNode(Node node) {
        nodes.add(node);
    }

    public void removeNode(Node node) {
        nodes.remove(node);
    }

    public Set<Document> search(String query) {
        Set<Document> result = new HashSet<>();
        for (Node node : nodes) {
            result.addAll(node.search(query));
        }
        return result;
    }
}

public class SearchEngine {
    private Cluster cluster;

    public SearchEngine(Cluster cluster) {
        this.cluster = cluster;
    }

    public Set<Document> search(String query) {
        return cluster.search(query);
    }

    public void addDocument(Document document) {
        // Determine which node to add the document to based on a specific strategy (e.g. round-robin, consistent hashing, etc.)
        Node node = determineNodeToAddDocument();
        node.addDocument(document);
    }

    public void removeDocument(Document document) {
        // Determine which node the document is currently stored on
        Node node = determineNodeForDocument(document);
        node.removeDocument(document);
    }

    private Node determineNodeToAddDocument() {
        // logic to determine the node
    }

    private Node determineNodeForDocument(Document document) {
        // logic to determine the node
    }
}