Adore that couch! A patterned rug would look great. You obviously have a bold sense of style, so keep going with it. Bold can still totally be elegant. IKEA has some a awesome, affordable options.

You can keep it neutral, with a bold black & white pattern, which will let your lime couch stand out and shine. You could go navy, which will make the room a little more sophisticated/chic. Or you could go casual and warm with a yellow.

I can't tell the dimensions of your room, but I'd guess you have room for an 8x10. Best of luck!

[houzz= https://www.houzz.com/photos/1958-mid-century-modern-living-room-remodel-midcentury-living-room-phvw-vp~396659]
You could do either, but your floors are a nice feature, and would look well without a rug, too.

I think this one is from West Elm

https://www.houzz.com/photos/7th-avenue-parkway-contemporary-remodel-contemporary-living-room-denver-phvw-vp~2934546

I'd go with a rug that will extend just a bit beyond the edge of the chaise. That way, you pull the room together and still show off those great floors. I'd pick a geometric addy metric something on a solid neutral bwckground, very mid century.

http://houzz.com/photos/134028 like that?

Yes.

I think I would first get throw pillows. Here are a few ideas:

http://deciture.com/biya-pillow/

http://deciture.com/essentials-marine-blue-pillow/

http://deciture.com/zeera-pillow/

I like that last rug - prefer one that has some of your sofa color in it - which I love.

I like every one of those rug suggestions. You have so many options! Which is nice.
You could even do something overdyed; this one is pretty reasonable at $536 for an 8 x 10.

White shag!

Beautiful! I think pattern is fine - but keep the rug light with some dark accents. I wouldn't incorporate any lime green or blues - but stick with a neutral palette of black brown and white. Here's a photo of a rug that might inspire you that I used in a project - totally different space but it shows how an off-white rug looks. Good luck from Montreal!

Thanks everybody!! That was really helpful! This is time first time I've posted here so very thankful for tne suggestions

The stripe one you have looks retro like the sofa...if you could fine a similar one with the lime green it would pull it together

A solid rug would be BORING. Definitely get a patterned rug with some of the green in it.

I don't think you need to have any lime green in your rug but some art on that big blank wall next to the windows with all your colors (couch and rug) could go a long way toward pulling things together. Then you need to have spots of those colors around the room to add even more continuity. I'm not sure that rug is placed to its best advantage in this photo.

How about some plants in large pots the colors of your couch and rug to go behind that white chair. You need to bring your colors to other areas of that space. What you have nicely reflects the outdoor colors but you need something in that area to ground things.