Writing in his book “A Christian Directory”, (something every pastor should consult) Richard Baxter talks extensively about Lent, he says in part:
It is not unlawful for those that cannot totally fast, yet to use more abstinence and a more mortifying sort of diet than ordinary, for the exercises of repentance and mortification, in due time.
[…]
As for the commanding such an abstinence, as in Lent, not in imitation, but bare commemoration of Christ’s forty day’s fast, I would not command it if it were in my power; but being peremptorily commanded, I cannot prove it unlawful to obey; with the aforementioned exceptions.
It was anciently held a crime to fast on the Lord’s day, even in Lent; and I take that day to be separated by Christ and the Holy Ghost for a church-festival or day of thanksgiving; therefore I will not keep it as a fast, though I were commanded, unless in such an extraordinary necessity, as aforesaid.