Is there any rules of thumb for the relation of number of iterations and training size for lightgbm?
I'm not aware of a well-established rule of thumb to do such estimate. As Florian has pointed out, sometimes people rescale the number of iterations obtained from early stopping by a factor. If i remember correctly, typically the factor assumes a linear dependence of the data size and the optimal number of trees. I.e. in the 10-fold cv this would be a rescaling 1.1 factor. But there is no solid justification for this. As Florian also pointed out, the dependence around the optimum is typically reasonably flat, so +- a bit of trees will not have a dramatic effect.
Two suggestions:

do k-fold validation instead of a single train-validation split. This will allow to evaluate how stable the estimate of the optimal number of trees is. If this fluctuates a lot between folds- do not rely on such estimate :)
fix the size of the validation sample and re-train your model with early stopping using gradually increasing training set. This will allow to evaluae the dependence of the number of trees on the sample size and approximate it to the full sample size.
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!