I am going to be really unpopular here. Catbells or Buttermere or any fell (hill) walk I can't say you should do in trainers, as they do not provide enough ankle support. I know that many people do, but Murphy's Law says that you are the one who will go over on your ankle and potentially have to be rescued by the volunteer mountain rescue services/even airlifted by helicopter.
I will say that I am one of the many stupid ones who do, because of a blood dis-order I cannot wear footwear that covers the ankles. But I know what I am doing and am willing to turn if I am, in my opinion, at too much risk. Lecture over.
Aira Force- unless something unexpected when the timetables come out you would have to go to Penrith (on the even hour from Keswick) then change at Penrith on to the #508 to Windermere (or of course the 555 to Windermere, then the #508 every odd hour towards Penrith). I don't expect the extra (even hours) 508 Open Top Buses Penrith to Patterdale to be running on weekdays in June.
That one is fine in trainers, You could then go down to Aira Force pier for the boat to Glenridding.
Castlerigg is fine in trainers. At the Penrith Road/Chestnut Hill junction you can join the K2T rail path in either direction (Threlkeld or Keswick Station). The K2T is now fully re-open after being destroyed in two major storm events since 2015. It had to be totally rebuilt. As "urban/suburban" hikers that would meet all your criteria except the lake views- and meet them in bucket loads. To me it is far and away the best short (3.5 miles) all abilities walk in the area. There is a bus stop at the trail end at Threlkeld, or wander into the village for the splendid tearoom in the Village Hall.
If you wanted to do the Lodore Falls take the open top bus one way and the launch the other way. That one, is short enough to do it in trainers.
You can get down to either Buttermere or Crummock lake at Buttermere village- I am just not happy with going round the lake. Then go the farm ice cream parlour afterward.
The other lake walk would be the 554 or X4 to Mirehouse (Hall)/Dodd Wood (for the Ospreys) then the walk down to the idyllically situated old St Bega's Church (by Bassenthwaite), maybe even visit Mirehouse. There is a theme here- with a good tea rooms at Dodd Wood car park.
You can extend the St Bega's walk on the back road through Scarness to Bassenthwaite Village for bus home.
In the other direction from Dodd Wood there is a woodland path, which takes you to the quiet byway through Milllbeck and Applethwaite back into Keswick- about 4 miles. That's the sort of walk you want.