When are lay men and women permitted to proclaim the Gospel in a Catholic church? I know that proclaiming the Gospel at Mass is restricted to ordained folks. But, is it permissible for a lay man or woman to lead a word and communion service and read from the Gospel? 

Can they lead a different sort of prayer service in a Catholic Church that includes the proclamation of the Gospel?
Well, at a minimum, most people read from the Gospel on Palm Sunday and Good Friday (only about four lines which are labeled "[said by the] crowd:"). I think that counts as laity ;-).

As to "communion service", the prayers of an EM with the homebound can be considered a "communion service," and anyone is allowed to read there.



Coming back to this post several years later. It should be noted that Mass is the only liturgical prayer of the church where the reading of the gospel is specifically designated to the clergy. In the normal form of the Divine Office, there is no gospel. There is, however, a canticle from Luke which is read or sung in common. In the Lectio Divina, sometimes prayed in conjunction with Matins, Vigils, or as a separate service, the gospel may be read by any in attendance, according to the norms of the particular community.

None of this is different from prior to the reforms of the liturgy under Paul VI. The Divine Office was open to all and supported a variety of expressions, even within the more restrictive hours (you can read more about the different liturgical approaches to Vespers here). The Lucan Canticles were said in common.

Preaching on the gospel, however, was a good deal more restricted. However, even in this case, there was a good deal of leeway. It is the task of the prior, whether ordained or no, to exhort the brethren while they eat. This implies 1. that a quasi-liturgy is in effect, and 2. that a non-ordained person is preaching.