Alice + Lewis would I think be a bit odd because of Alice in Wonderland, and yes they are very similar sounding names.
Plus as others have said an Alice might well become Ally or Al. Very difficult to find names that can't be shortened, and lots of children like nns too. I think it's better to choose a name where you like the nns really.
My grandmother had similar views, and called her children Ian and Clare. They both were known by nicknames throughout their childhood!
More helpfully I think that the hardest names to shorten are single syllable names. You might find they get lengthened instead though.
Whatever you call your child, don't underestimate the ability of other children, especially teenagers, to find a nickname - if they can't shorten it, they will lengthen it - Mae will become Maisie, Bet, Bezza etc.
I thought no-one would shorten 'Amber' when we called DD that - she's been Bambi, or Bam ever since she went to secondary school...
Emily (although they often get "Em") Esther Heather Eve Anna Ruth
Although I think if you really love Alice, you should go for it, it doesn't sound too strange with Lewis. If you love the name Alice, unless you find something else you love more, you're going to always think of her name as a compromise.
I know to Alices, one sticks with Alice, the other is universally known as Ali. Lewis and Alice is a bit of a mouthful when said together but they don't sound so similar you would constantly be getting the wrong one when you call up the stairs.
Also, names that are already short tend to get lengthened, either to their "correct" name eg Meg to Megan, or just because they sound too short, eg Ann to Annie, Grace to Gracey, Jane to Janey.