Here is the calculator. There is a learning curve but it can become addictive. The hardest part for me, once I figured out how to manipulate it, is to determine what genetics to start with. The calculator makes some assumptions but there are often different ways genetically to get a color. Also, it assumes the genetics are pure, that there are no recessive genes hiding under dominant genes. Unfortunately that is not always the case. It does not handle leakage and some of the strange things that can happen when genes mix either. Still it is a great tool to get a handle on basic genetics.
Cross Calculator
http://kippenjungle.nl/Overzicht.htm#kipcalculator
Your Lavender rooster should be based on Extended Black. That is almost but not quite a certainty. He could have Birchen with Melanizers but that would be rare. He may have something other than Extended Black hiding at that location on the chromosome, masked by the Extended Black. But it is a pretty safe bet he has Extended Black and you have to assume he is pure for that.
Lavender is a recessive gene. Any effects from that will disappear in the next generation. For deciding what his babies will look like, assume he is black.
Chocolate is a funny one, with some stuff going on at the Dominant White gene location. It’s also based on Extended Black. Half the offspring should be black, half chocolate.
Blue Copper is Birchen with the gold gene. Blue is a strange one where two copies of that gene at that gene location will give you Splash, one copy gives you blue, and zero copies give you black. The blue and splash only affect feathers or parts of feathers that would normally be black if that gene was not present. The Extended Black will overpower the Birchen and give you solid colored chicks. The gold might give you some leakage where a few isolated feathers show up some shade of red. Half the offspring should be blue, half black.
I don’t know for sure how you make Iowa Blue but I’d assume half the offspring will be black, half blue.
With the Splash hen, you will get all-blue chicks. They should be solid blue.
I don’t have a handle on the White Crested Blue Polish genetics. A guess is that the chicks will be half blue, half black and you will see the effects of that crest. It depends on what that “White” is though. It’s possible you could get solid white chicks. White can do funny things.
With the Black Cochin, they will all be black. If the hen is pure for the feathered legs, all her offspring should have feathered legs.
There is some guesswork involved in this but I’d expect you to see a lot of black, quite a few blue, and hopefully a chocolate or two thrown in. Good luck!