Since the StackOverflow link in the question comments seems broken, here is another reply that addresses the same question: https://stackoverflow.com/a/44789327/6470915
In fact, Blei (who developed LDA), points out in the introduction of the paper of 2003 (entitled "Latent Dirichlet Allocation") that LDA addresses the shortcomings of the TF-IDF model and leaves this approach behind. LSA is compeltely algebraic and generally (but not necessarily) uses a TF-IDF matrix, while LDA is a probabilistic model that tries to estimate probability distributions for topics in documents and words in topics. The weighting of TF-IDF is not necessary for this.
That sums it up on the high level. It would be interesting to understand more technically, why the model would perform more poorly if TF-IDF is used. Actually, there is another reply in the SO link which claims that LDA can be improved with TF-IDF.
LDA is a word generating model, which assumes a word is generated from a multinomial distribution. It doesn't make sense to say 0.5 word(tf-idf weight) is generated from some distribution. In the Gensim implementation, it's possible to replace TF with TF-IDF, while in some other implementation, only integer input is allowed.