Welcome to Lustria! You've come to the right place for advice.
Firstly, it's not a terrible list. It won't be competitive though. Definitely some areas for improvement.
I like the magic of the Lizardmen, so usually I have a slann but there just weren't enough points to have a slann and Engine of the Gods and to have support guys in my units, which I have been told that they are important in the 8th ed.
Hmmm... I don't follow your logic. Are there restrictions to the rules for fielding an army that you haven't posted? Because if not, you have 550 points to dump on a Slann and 550 for your EOTG. Heck, you have enough to run two naked Slanns while still including an engine. If there are restrictions, I would favor a Slann over the engine any day. ESPECIALLY in a tournament. He is a much better support character.
For the rest of the list:
Characters look ok. You don't need a BSB, though it is a good idea to bring one. That means you need a Slann, Scar-Vet, or a Chief.
16 skinks will just hold up any other unit for half of a round of close combat. I'd either give them some Kroxigor or turn them into Skirmishers. Otherwise just drop them.
Cold One Riders are a huge point dump for non-friendly games. Drop them. You can get yourself some chameleon skinks and another pack of Salamanders for the same price or less.
And a couple of final thoughts for you;
1. Two stegs are better than one
2. You can never have too many saurus (unless you have one unit of 100 guys or something crazy