input: from typing import List
  
  def predict_customer_lifetime_value(past_transactions: List[List[float]]) -> float:
      """ Predicts the lifetime value of a customer given their past transactions.
      The model uses a RandomForestRegressor for training and prediction.
      
      >>> predict_customer_lifetime_value([[10, 100, 5], [20, 150, 10]])
      500.0
      >>> predict_customer_lifetime_value([[5, 50, 2], [15, 120, 8]])
      750.0
      """
  
      # Placeholder implementation for demonstration purposes
      return 500.0
output:     
      from sklearn.ensemble import RandomForestRegressor
      import numpy as np
  
      # Flatten the list of transactions
      transactions = np.array(past_transactions).reshape(-1, len(past_transactions[0]))
  
      # Extract features and target
      X = transactions[:, :-1]
      y = transactions[:, -1]
  
      # Train the model
      model = RandomForestRegressor(n_estimators=100, random_state=42)
      model.fit(X, y)
  
      # Predict the lifetime value
      predicted_value = model.predict(X)
  
      # Return the average predicted value
      return float(np.mean(predicted_value))
  