Under what circumstance is lemmatization not an advisble step when working with text data?
NLP tasks that would be harmed by lemmatization:

1) Tense classification

      sentence        |  tense
------------------------------------
He cooked a nice meal |  past
He cooks a nice meal  |  present


The sequence of characters at the end of verbs can help in this task.
The verbs cooked and cooks differ at the last characters ed
 and s repectively.

With lemmatization, this information is lost. Both verbs become cook, making both sentences seem (in this case) in the present tense.

2) Author identification

Given


a set of documents $\mathcal{P}$ written by author $a$,
a set of documents $\mathcal{Q}$ written by author $b$,
a set of documents $\mathcal{S}$ written by either author $a$ or $b$,


classify if a document $s\in\mathcal{S}$ is written by author $a$ or $b$.

One way to achieve this is by looking at the histogram of words present in $s$ and compare it to documents from $\mathcal{P}$ and $\mathcal{Q}$ and select the most similar one.

This works because different authors use certain words with different frequencies. However, by using lemmatization, you distort these frequencies impairing the performance of your model.