I have following sentence
お風呂に入ってから、ゆっくりしたり、本を…。[読む]
After taking a bath, I want to do things like relax and read books.
Why this is correct
お風呂に入ってから、ゆっくりしたり、本をよんだりしたい
and this is wrong
お風呂に入ってから、ゆっくりしたり、本をよみたりしたい
Why do I need to use て form with 読む?
たり～たりする uses the past tense of the verb, in this case 読む.
The correct conjugation of 読む into past tense is 読んだ.
Hope that helps 
I think you misread the correct answer. It’s not te-form. You have the right idea, you just have the incorrect past-tense form of 読む
Now it’s very clear. Thank you all of you.