We are lakes lovers - go every Autumn (more if we get the chance!).
Our DS is 7 now but some things we do/have done and enjoyed:
Grasmere - nice little play park there which will be good for your 4 year old. Picnic tables to sit at. It's a nice village to have a little wander around.
The Bobbin mill at (if I recall correctly Newby Bridge). Went last year and it was brilliant! Not too big but really interesting and the guide was fantastic with children and explained things to their level. Our son loved it and they let children choose a bobbin to take home.
Bit further afield (and the drive is not for the faint hearted!!) but well worth a visit is Eskdale mill. It has a working waterwheel and a small model one for children to play with outside. Again, fairly small but lovely, knowledgeable guides. Village pub there was nice for lunch.
Keswick fun pool is good and fairly cheap. Check booking arrangements with covid. Get there for the start of the session. Nice gradual entry and there is a wave machine.
Also the lake at Keswick (near the theatre) is nice for a stroll. There is also an optical illusion place at Keswick which was fun! Plus a nice park. Never had much luck eating in Keswick but the Mary Mount hotel nearby is excellent.
Park at windermere is good for kids. Bowness is nice for a stroll round but don't attempt it with a pram (voice of bitter experience!).
Threkeld mine was another good trip.
Aquarium and steam train at Lakeside are good for little ones.
Ambleside is a nice town but we haven't stopped there for a while as it's always rammed! If you're patient enough to wait for a parking space though, it's nice.
Kendal is lovely. On Wednesday and Saturday morning, the Unitarian chapel do coffee/tea/scones - all welcome.
Grizedale forest and aira force are both great.
If you're after a good meal, the Sun at Crook is highly recommended 
Missing the lakes having typed all that! Roll on October when I'm going 