The correct answer is $\boxed{\text{A}}$.
When a body is weighed by a spring balance in a moving lift, the reading on the spring balance is less than the actual weight of the body if the lift is accelerating upwards. This is because the upward force exerted by the lift on the body is greater than the force of gravity acting on the body. The difference between the two forces is equal to the mass of the body times the acceleration of the lift.
In this case, the body appears to weigh 13 g when weighed by a spring balance. This means that the upward force exerted by the lift on the body is 13 g. The acceleration of the lift is therefore equal to the force exerted by the lift on the body divided by the mass of the body. The mass of the body is 14 g, so the acceleration of the lift is 13 g / 14 g = 0.5 m/s^2.
Option B is incorrect because the acceleration of the lift is less than 0.7 m/s^2. Option C is incorrect because the acceleration of the lift is greater than 1 m/s^2. Option D is incorrect because the acceleration of the lift is not equal to 1 cm/s^2.