A strategy Bety can take is to split the cake in a way that one slice has her favorite topping but its smaller than the other slice of cake.
How many times smaller? Enough to make her indifferent between the bigger slice and the one that has her favorite topping.
The reason for this is that if Lucy picks the smaller size that has Bety’s favorite topping, Bety would’t mind because she will have a bigger slice.
If Lucy picks the bigger slice, Bety wouldn’t mind either because she will have the slice with her favorite topping.
All this assuming that there exists a portion of the cake, without her favorite topping but big enough, that if consumed would give her the same utility than consuming the smaller portion with her favorite topping.