Adding a indoor concrete ramp to existing concrete
As I understand it, your laundry room connects to another room with basically a smooth level concrete floor.... and you want to create a "lip" in the doorway to prevent water escaping the laundry room.

To state the obvious:  the real trick would be to prevent the flooding in the first place.  Why does it flood?  Is there a drain that could be improved?  

Aside from that, let's turn the conversation around.  What you're describing is kinda like a very low shower-stall enclosure.  If you can shift your thinking to 'how would I make a 1-inch lip to enclose a shower', you might start thinking about other options:


something made of tile (grouting into place to get a good seal on the sides and bottom)
some plastic pre-made shower seal that might be cut to length (link: https://www.amazon.com/Wide-High-Acrylic-Frameless-Threshold/dp/B0031Q4DF8 )
even enclose the 'flooding area' (like a washing machine) with a water-catchment basin (like many people do for water heaters) might be a solution


Hopefully this is of some use to you.  Good luck!