The question of whether or not a woman can "lead worship" is determined by two things. 1) How you understand what Scripture says about male leadership; and 2) how you understand the role of the worship leader. Our culture has worked overtime to persuade us that there is no difference between male and female leadership, or at least that men and women can lead in any situation. I think the Bible disagrees. Here are some relevant Scriptures:
1 Cor 14:34-35 "women should remain silent in the churches. They are not allowed to speak, but must be in submission, as the Law says. 35 If they want to inquire about something, they should ask their own husbands at home; for it is disgraceful for a woman to speak in the church."
1 Tim 2:11-15 "A woman should learn in quietness and full submission. 12 I do not permit a woman to teach or to have authority over a man; she must be silent. 13 For Adam was formed first, then Eve. 14 And Adam was not the one deceived; it was the woman who was deceived and became a sinner. 15 But women will be saved through childbearing--if they continue in faith, love and holiness with propriety."
Titus 1:6 "An elder must be blameless, the husband of but one wife, a man whose children believe and are not open to the charge of being wild and disobedient."
The Bible clearly teaches that the role of Pastor is reserved for those who meet the qualifications laid out in 1Tim 3. Since one of these requirements is to have a wife as your spouse, it is impossible for a woman to meet these qualifications. Furthermore, the Bible commands women to teach other women and not to have authority over a man in the church.
Because there is no “worship leader” role in Scripture, we have to determine what biblical roles it fulfills. Sovereign Grace see the role of the worship leader primarily as a pastoral responsibility. Those who lead congregational worship will fulfill at least four functions: leading, pastoring, teaching, and prophesying. Only prophesying is specifically a male/female gift. The others are defined as male functions in a mixed gathering. Of course, church environments exist where the leadership does not want the worship leader teaching, pastoring, etc., or at least they do not function in this way. A church may have a “music leader” that does nothing but play an instrument and lead rehearsals. Perhaps a pastor is more involved in the singing portion of the meeting, or the "worship leader" is more of a "song leader," or the comments made by the leader are confined to more brief spontaneous encouraging comments. In those situations the male/female distinctions are minimized. However, in our understanding, there would always be a tension between what a leader could do, and possible misunderstanding regarding a woman's leadership role in the church. Of course, a woman can lead worship in a women's meeting, or in children's ministry, or can be a major contributor as part of a worship leading team. It also seems possible that a woman could lead worship in a small group, where the leader is exercising clear directional and pastoral authority.
In any case, God’s desire isn’t to limit our serving, but maximize it by seeing us function to the fullest extent in the complementary roles that he has ordained for us.