Suggestion on LDA
I have worked on similar lines. This approach can work till 300 such documents. But, taking it to higher scale you need to replicate the approach using spark.
Here it goes:
1) Prepare TF-IDF matrix: Represent documents in terms Term Vectors. Why not LDA because you need to supply number of themes first which you don't know first. You can use other methods of representing documents if want to be more sophisticated (better than semantics) try word2Vec, GloVe, Google News Vectors etc.
2) Prepare a Latent Semantic Space from the above TF-IDF. Creation of LSA uses SVD approach (one can choose the kaiser criteria to choose the number of dimensions). 
Why we do 2)?
a) TF-IDF is very sparse. Step 3 (tSne) which is computationally expensive. 
b) This LSA can be used to create a semantic search engine
You can bypass 2) when your TF-IDF size is very small but i don't think given your situation that would be the case and also, you don't have other needs like having semantic search on these documents.
3) Use tSne (t-stochastic nearest embedding) to represent the documents in 3 dimensions. Prepare a spherical plot from the euclidean cordinates.
4) Apply K-means iteratively to find the optimal number of clusters.
Once decided. Prepare word clouds for each categories. Have your themes.
I am trying to do textual analysis on a bunch (about 140 ) of textual documents. Each document, after preprocessing and removing unnecessary words and stopwords, has about 7000 sentences (as determined by nlkt's sentence tokenizer) and each sentence has about 17 words on average. My job is to find hidden themes in those documents. 
I have thought about doing topic modeling. However, I cannot decide if the data I have is enough to obtain meaningful results via LDA or is there anything else that I can do. 
Also, how do I divide the texts into different documents? Is 140 documents (each with roughly 7000 x 17 words) enough ? or should I consider each sentence as a document. But then each document will have only 17 words on average; much like tweets. 
Any suggestions would be helpful. 
Thanks in advance.