This is not advisable.
Please be careful when doing this.
Lemon juice is acidic.
It is VERY acidic.
Although it may have an alkalizing affect on the body it is NOT good for your teeth.
If you drink lemon juice in water you are essentially drinking something acidic - at least while it is in your mouth.
That type of acid can attack tooth enamel and increase bacterial growth (the bad bacteria). When the bad bacteria get a more acidic environment they reproduce faster.
The bad bacteria then secrete acidic waste products. This makes the mouth even more acidic.
Many fruits, like lemon are believed to have an alkalizing affect on the body. However, many of them are acidic while in the mouth.
You have to consider everything that is happening, not just the end result.
If you want alkaline water, read this blog post.