I am copying my answer from previous posts and tailoring it to your question, just an FYI
Putting your Question into Context
To answer your question, we have to ask "Were Christians persecuted the way that the Christian Churches explain it today?" This is a valid question since Christian tradition teaches that Christians came under heavy persecution throughout their early existence. Being martyred and being thrown into gladiatorial battles is often envisioned and cited whenever I ask my students (I'm a teaching assistant at a university) what they thought the early years were like. However, this isn't the most reasonable assessment nor is this belief held by most scholars.
A truly excellent book on this topic was by historian Candida Moss, whom wrote The Myth of Persecution: How Early Christians Invented a Story of Martyrdom. Here, Moss (a professor of New Testament Studies at Notre Dam) argues that there was never a wide-spread persecution of Christians as most people believe. Of the over 250 years of Early Christian history, Moss presents evidence that at most there were only 12 years (at most) where people were harshly persecuted for their faith by orders of the Roman Empire (none of them coming in the first century, during the early conversion times). For it's first few decades, Christians probably went relatively unnoticed. Small churches were known to have sprung up throughout the eastern Mediterranean and even at least one in Rome by 70 CE (this is about when and where Mark wrote his gospel), but it is unlikely Christians faced any real threat yet since they weren't converting huge percentages of people in their populations.
As Christianity became more popular, most likely by the end of the first century, it is likely that this is when they started facing harsher criticism. Most were simply scorned or disliked, similar to hows Jews were treated once they left the Levant. For most early Christians, "the vast majority of Christians never stood before a Roman judge, paid a fine, or experienced torture," [Moss, page 129] however, some did. Moss, and other historians, have pointed out that persecution did take place in several locations around the Roman Empire, but again, this is more the exception to the rule. The reason for this is simple, "For almost all of the first century, it’s unclear that Roman emperors even knew that Christians existed," [Moss, page 139] meaning that you can't persecute and hate something that you didn't even know existed.
I will add that there were some specific areas and period of persecution where select numbers of Christians were tortured or even killed, but this didn't happen until the second century, and was rare and didn't last for very long. For the most part, Christianity was a small sect that didn't expand considerably until Constantine, and for the most part, they didn't really pose as a serious threat to Rome.
Macrus Aurelius's involement
Now for you specific question, the short answer is: he wasn't very involved at all. Marcus Aurelius (to our knowledge) had no vendetta against Christians, yet at the time, certain Roman Provinces (such as North Africa) were experiencing mild to moderate forms of persecutions by local leadership, but nothing by the orders of Marcus Aurelius himself. It should also be noted that Christianity was very small at the time -- at best maybe 1% of the Roman population (and probably much smaller), so they were overall not very important to him by this time period. However, he was aware of some complaints since the man known as Saint Justin wrote an open letter to the Emperor himself, where he defended Christians and stated that they were being persecuted for nothing more than “for their name,” and not for any actual crimes. [Justin, First Apology 4.4.]
TL:DRHowever, historically speaking, again, real persecution was a conversion tool to influence people into joining Christianity (people would think, "if so many people are willing to die for this message, it has to be real!"), so like all the other time periods persecution under Marcus Aurelius was not done under his orders nor were they heavily present.
TL:DR: While it is likely that some Christians were killed by lions or other similar beasts, it rarely happened over the first two and a half centuries of Christianity's existence.