hey, well I agree with brocky in that if you are going to cross breed make sure you can take responsibility for every bird they produce for their entire lives because they are likely to be unsellable.
If you are doing it just for you enjoyment of colour, go ahead, but like was said physical traits will mix, and it will not mix to give you the best of both worlds.
That being said, I'm pretty sure your Lahore is not pure. His colouring is completely off mark and his body structure is much more slender and streamlined than it should be imo.
As regards colour;
They are both blue based, so you will get blue offspring.
They may of course carry something recessive like rec red or rec white but you won't know until you breed them, and they'd have to both carry it for anything to show.
So you will 90% likely get blue birds.
The male has the spread factor (no tail bar) maybe het or ****, the female does not (though I do not know if she is bar, barless or check)
The female also carries grizzle I believe. Male definitely carries some whitening, but I do not know enough to tell you if they are just pied or a specific gene
So you will get blue birds with white markings - grizzle is dominant so all offspring should end up with it (so far as I know)
If the male is split for spread, then half the young will be spread, half not.
If he is a homozygous spread all the young should be solid blacks (base colour)
The white markings are a lot more random and difficult to predict. You could get anything from a very white bird to a bird with a few splashes of white.