How can we solve it for the value of current Ia?
There's no contradiction in this:

$$I_4 = -0.5(I_4 - I_3)$$
$$1.5 I_4 = 0.5 I_3$$
$$I_4 = \frac{0.5}{1.5}I_3$$

When you add the equations for meshes 1, 2, and 3, you'll be able to get the solution in terms of \$V_1\$.