Maybe-but the question is asked the wrong way around. The starting point is what are the features of rainfall runoff that are of interest and, then, the question can be asked, what are the networks that can extract them.

Thinking of it in a mechanistic manner, the Rainfall-Runoff relationship is determined by evapotranspiration and moisture storages, which are related among themselves as well. In the traditional tank model formulation, runoff is modelled using a cascade of tanks which have different outflow coefficients. The outflow from these tanks are dependent on the amount of water in the tank and the coefficient. The outflow put together is the runoff. So, assuming what you want is to predict runoff when only rainfall is available, you can either use the classical tank model or regressions. LSTM is also a sophisticated regression, in essence, but by looking into memory, it's layers might be able to "guess" the soil moisture state (which determines runoff). Simply, you may just be able to predict the runoff from rainfall alone. If you want to include other factors, use factors that affect the soil moisture storage (e.g., soil properties), evapotranspiration (e.g., vegetation properties), or land characteristics (e.g., topography).

I think most kinds of ANNs could well simulate the river discharge with the previous observed streamflow and current rainfall data. But those works highlight the predicted discharge only. Hence, if for something new, your point should focus on if the LSTM can reasonably reflect the mechanistic processes. Specifically, the soil moisture has the memory of previous wetness in a watershed, which may be suitable for the function of short-term memory in LSTM. It means soil moisture productions made from remote sensing or land surface modeling may be useful for your research project. Moreover，some of my work published in 2013 and 2014 could be helpful, as well.