Martyn Lloyd-Jones addresses this much better than I could. I've long disliked the idea of a "lay elder" or "lay preacher", or in other words, a guy who works with computers during the week and then somehow on Sunday is competent enough to lead a congregation in worship? Give me a break.
If I go to see a doctor, it's a doctor who is full-time in his practice, not a guy who practices medicine "only on Sunday". From Chapter 6 of "Preaching and Preachers" (p. 100) (my highlights added)
The first principle I would lay down is that all Christians are
clearly not meant to do this, and that not even all Christian men are
meant to preach, still less the women! In other words we must consider
what is called 'lay-preaching'. This has been practised very
commonly for a hundred years and more. Prior to that it was comparatively
rare, but it has become very common. It would be interesting to go into the history of that, but time prohibits our doing so. The
interesting thing to notice is that this change once more, was primarily
due to theological causes. It was the shift in theology last century
from a Reformed Calvinistic attitude to an essentially Arminian one
that gave rise to the increase in lay-preaching. The explanation of that
cause and effect is that Arminianism, ultimately, is non-theological.
That is why most denominations today are generally non-theological.
That being the case it is not surprising that the view gained
currency that preaching was open to almost any man who had become
a Christian, and later, any woman also.
My assertion is that this is an unscriptural view of preaching.
There are of course exceptional circumstances where this may be
necessary; but I would then query as to whether it is actually 'laypreaching'.
What I mean by exceptional circumstances is that it may
well be the case, owing to the state and the condition of the Church lack
of means and so on-that the Church may not be in a position to
support a man full-time in the work of the ministry, and particularly
preaching. Definitions are important at this point. The modem view
of lay-preaching, largely derived from the teaching of Methodism and
Brethrenism, is that this should be the normal practice and not the
exception, and that a preacher is a man who earns his living in a
profession or business, and preaches, as it were, in his spare time.
(Also helps reinforce the idea that Methodists often get things wrong, too)