Vectors and lists are data structures. SQLite columns only accept atomic values, namely numbers, strings and blobs.
Therefore you need to serialize (convert) the vector/list into a single string or blob - numbers won't do anyway. You will have to use an encoding that is uniquely reversible and will preserve any special properties of your data structure.
Sure, you can re-invent the wheel and use your own encoding. Or you could semi-reinvent the wheel by using the Java Serialization API. Or you could use something like JSON, which is a more tried solution.
If I were you, however, I'd first consider changing the database schema. Lists and vectors are close enough to the relational model that you might be able to store them in the database without serialization techniques.
EDIT:
See also this question and this one.