Yes they can and are encouraged to do so basically because of the hadith saying:
One who is proficient in the Qur'an is associated with the noble, upright, recording angels;
- and he who falters in it, and finds it difficult for him, will have a double reward. (sahih Muslim and Sunan ibn Majah)
- and he who falters when he recites the Qur'an and finds it difficult for him will have a double reward. (Sunan abi Dawod)
- Hisham said: "And it is hard for him" - Shu'bah said: "And it is difficult for him, - then he gets two rewards." (Jami' at-Tirmidhi)
- and he who falters in it, and finds it difficult for him, will have a double reward. (sahih Muslim and Sunan ibn Majah)
- and he who falters when he recites the Qur'an and finds it difficult for him will have a double reward. (Sunan abi Dawod)
- Hisham said: "And it is hard for him" - Shu'bah said: "And it is difficult for him, - then he gets two rewards." (Jami' at-Tirmidhi)
Here you may see that at-Tirmdihi quoted that some narrators paraphrased what they heard. This doesn't mean that they heard something different, but could mean that they didn't recall the exact words they've heard.
So on the whole who ever does efforts to read/recite the Quran would get a reward for this especially if he has some issues like stuttering, lisps or can't speak Arabic.
Note that some speech impediments can be cured or treated and Arabs used to dislike hearing speeches of people who lisps so in some cases tribes used to break the teeth of the spokesmen of their enemies if they were too eloquent.