Hi Fluttershy, We are a family owned group of hotels in the Lake District which are family friendly. We have a baby-listening service which means that in the evenings you can put baby to bed and you and your partner can have a bit of time together and enjoy dinner in the hotel restaurant and have your baby listened in on. Have a look here - www.lakedistricthotels.net/childrens_breaks.php
Hope that is also helpful in your decision to come to the Lakes!
The Lake District with DC is fantastic. I found it really hard going with tiny ones. Hard to find things to do. I'm quite happy for Dc to get soaked to the skin, but not so sure about babies. Agree you need a carrier, even in towns, the pavements are too narrow and crowded for a pushchair.
See if you can get a weeks membership for one of the hotel health clubs if you're not staying somewhere with a pool, then at least you can swim when the weather's awful (although I'm sure you'll get wonderful weather Other than that, get a book on low level or waterside walks. We're quite adventurous walkers, but my bottle went when it came to taking a tiny one into the hills.
I love the Lake District and so do my DC. we're going on a our first foreign holiday in more than 10 years this year, but it was very much booked on the condition that we can manage a week in the Lakes too. Have a great time