How to encrypt a vector $e\in Z^{m}$ using LWE I have a vector $e \in Z^{m}$, now I want to encrypt it by using LWE (Learning With Errors).

Because in LWE, we have to encrypt of a bit $\{0,1\}$. How can I encrypt a vector $e \in Z^{m}$?
I think you will not find any scheme that works over $Z$. 

But, if you want to work over $Z_t$, you just have to choose a LWE-based encryption scheme that encrypts non-binary messages, and there is a lot of them!

For example, the paper ML Confidential uses one scheme  like that (non-binary messages) to perform classification algorithms over cipher texts.

The same occurs with this one: Using Homomorphic Encryption for Large Scale Statistical Analysis.

In general, the LWE schemes are presented considering only binary messages because the authors want to extend them to some Fully Homomorphic Encryption (FHE). Since the FHE is able to process functions described as boolean circuits, these schemes just worry about encrypt bits.

But usually, it's easy to change the schemes to work over $Z_t$ if you don't need a FHE, I mean, you don't need to do arbitrary sequences of multiplications and additions. 

To do so, you just have to adjust the modules used by the schemes and be aware that you possibly will be able to do less operations than specified on the papers to the same set of parameters.