I am trying to build an LSTM model to generate Shakspeare-like poems. I have data set $\{s_1, s_2, \dots, s_m \}$, which are sentences written by Shakespeare, and for each sentence, it contains words $\{w_1, w_2, \dots, w_n \}$. 

I have the following questions.

1. Are different $s_i$ ($i=1, \dots, m$) independent and identically distributed samples (IID)? Are $w_i$ ($i=1, \dots, n$) within each sentence the IID?

2. To my understanding, the cross-entropy loss (maximum likelihood estimation) can only be used when a random sequence is IID, but here the $\{w_i \}$ sequence is not (it's non-Markov, therefore non-IID, I believe), so I am suspicious on using cross-entropy for the task. Please, correct me if I am wrong.