It is normal for turtle waste to be very messy, disgusting, and stinky. Even solid waste may fall apart and appear to be "diarrhea." Keeping their home cleaner requires either changing all the water every day or two, getting a larger tank or pond, adding filtration (still requires water changes too), or feeding the turtle in another container of warm water as turtles defecate mostly after eating and also in warm water.
Also, lettuce isn't a great food to give turtles and can make their stools more loose than normal. Never feed iceburg lettuce. Green leaf lettuce and other green lettuces are ok to feed on occasion but shouldn't a major part of their diet. Try not only the commercial pellets but things like earthworms, grapes, kale, etc. My turtle pages at
http://www.fishpondinfo.com/turcare.htm#feeding talk more about foods to try.
I don't know that acidophilus would do much of anything.