Some lectors may not be willing to read petitions they're uncomfortable with. Those that are biased or slanted in some way, either politically or socially.
One way to handle these incidents is to arrive early before Mass, take ample time to read through the petitions and if you've got a problem, tell the sacristan or presider right way so they can have another lector read them.
Better yet, if you know in advance that you'll be reading the petitions, ask your liturgist or priest a day or two ahead of Mass to see them as soon as they're written. You may not control what they say, but you can choose whether or not to read them.
And if you ever feel that your parish's prepared petitions are too sensitive or offensive, remind those in charge about websites such as USCCB's on permissible intercessions, and others by Googling "Prayers of the Faithful guidelines."
The most "unwise" thing a lector can do is to change the petition wording up at the ambo on the fly, especially if your pastor had his hand in crafting the petitions.