No, it doesn't. The Greek word used is a nominative form ponerou and means the evil one, the satan; it certanly does not stand for "trouble and disease."
The same is evident from Slavonic version: "но избави нас от лукаваго"(but rescue us from the evil one)
This is correct both because of the word used and because a definite article is used. The proper translation is "the evil" or more forcefully "the evil one". The article got lost in Latin translation, as Latin has no articles, and it should have been restored in English. Another reason not to read the scripture alone.