I grew parsley & basil in a large 5 gallon bucket last year - in fact the parsley is still going strong in my garage. I have a coworker that buys a lettuce mix from one of the box stores every spring, and grows the lettuce in a half barrel along her driveway (she lives in a condo)
I think your lettuce & stuff should do just fine in the planter - and as already mentioned, the smaller carrots ought to love a potting mix or soil/compost mixture.
I think that many of us gardeners are finding raised gardening and/ or container gardening a very convenient way to grow veggies. What previously has been thought of as only for flowers - has expanded to include fruits & vegetables. Heck, if I can plop a tomato plant in my flower garden, I can stick veggies in a bucket!
I especially like that I can move things around as necessary. ~Jan