Yes, Great Lent is a period of Fasting. there are four major fasts during the year: Great Lent, The Apostles Fast (from the week after Pentecost till the Feast of Saints Peter and Paul), the Dormition Fast for the two weeks prior to the Feast of the Dormition of the Mother-of-God, and the Christmas Fast for the 40 days leading up to Christmas. Plus almost every Wednesday and Friday of the year. On most Fast days, you can't eat any animal products, but on some days, fish is allowed, in particular if it coincides with a major feast day of a Saint for which there is a Liturgical Service. Being often in poor health however, Alexei would quite often have been exempt from the stricter rules of fasting, I would imagine.