Is there any rules of thumb for the relation of number of iterations and training size for lightgbm?
As you said in your comment, this is not comparable to the Deep Learning number of epochs because deep learning is usually stochastic.
With LGBM, all parameters and features being equals, by adding 10% up to 15% more training points, we can expect the trees to look alike: as you have more information your split values will be better, but it is unlikely to drastically change your model (this is less true if you use parameters such as bagging_fraction or if the added points are from a different distribution).
I saw people multiplying the number of iterations by 1.1 (can't find my sources sorry).  Intuitively this makes sense to add some trees as you potentially add information. Experimentally this value worked well but the optimal value will be dependent of your model and data.
When I train a classification model using lightgbm, I usually use validation set and early stopping to determine the number of iterations. 
Now I want to combine training and validation set to train a model (so I have more training examples), and use the model to predict the test data, should I change the number of iterations derived from the validation process? 
Thanks!