As we start Lent, we are asked to either give up something or begin some practice that deepens our connection with God. In modern relationships, which are celebrated on Valentine's Day, we usually have to either give up something or begin new practices (often both) as a way to show our devotion to our loved one. In both cases, this should be done willingly, even joyfully, rather than as a sacrifice. If we make a big show of these changes we make in our lives, or spend time complaining about the sacrifices that we feel we had to make, then those sacrifices have no real meaning as our complaints put up barriers between us and our object of affection.
Thus, both of these feasts are about establishing relationships and proving our dedication to them. I suppose it is such a strange matchup after all.