1. Run: Swiftly Racerback TankI think the Swiftly Tech fabric is the lightest, coolest and most breathable fabric Lululemon makes. Sweat dries very quickly and it has Silverescent in it so it's odor resistant. The Swiftly racerback tank has an open back which helps keep you cool. Unfortunately, this tank has an odd fit - very large armholes and long straps that make the tank fit very loose on top but the bottom is snug. It's hard to size down without the bottom fitting odd. Your bra will show under this. I wear an All Sport bra when I wear this tank. One drawback to this fabric is that it can snag easily. I wash mine in a mesh bag to make sure it doesn't get caught on anything.
2. Run: Energy Sleeveless - Anything Silverescent is great
I'd probably rank Silverescent as the second coolest fabric. It's very lightweight, breathable, and stretchy. If you are outside, it might be the most coolest because of the little holes that let air flow through it. There are two minor drawbacks to this fabric: 1 - Perspiration shows up very noticeably in the fabric - probably the most of anything Lululemon makes. 2 - The silver woven through the fabric can sometimes be very obvious. That may not bother most people but it's a pet peave of mine.
3. Luxtreme - Run: Zoom Singlet Tank & Run: Zoom Knee Short
I would rank Luxtreme and light luon as in nearly a tie for coolness and breathability. I give Luxtreme the nod because of it's great wicking ability. Luxtreme is very lightweight and stretchy. It feels great on but also is more revealing of imperfections. Some colors feel more lighter weight and stretchier than others (bubbilicious, angel blue, and potion seem lighter to me, the stripes and black are a bit heavier).
4. Light Luon - Cool Racerback
Light luon is awesome for hot weather workouts. Not nearly as bulky as the regular weight luon, but still provides a decent amount of coverage to hide imperfections.
Special Mention - Circle Mesh and No Limit Tank
If Lululemon made more than a handful of tanks in circle mesh I'd have to rank circle mesh as nearly equal in coolness and breathablity to silverescent. There have been a few tanks with significant amounts of circle mesh in them - The No Limit tank is all circle mesh over an attached Flow Y. Last summer's Sequence tank has a circle mesh body and luon top. The Conditioning tank also from last summer has a circle mesh back and luxtreme front and top. Both of those tanks are favorites of mine for summer workouts. Although Lululemon claims to have some sort of special odor fighting substance (chitosan?) embedded in circle mesh, on me circle mesh really retains odors and I have to wash my shirts and jackets with circle mesh armpits right away.
Luon Sheer Jersey - Sheer Delight Tunic
Luon sheer jersey is another extremely lightweight, breathable fabric. However, there haven't been many tanks made in this that are applicable for use in moderate impact cardio activities. Most of the tanks using luon sheer jersery have been designed for hot yoga classes. I thought the material felt great - soft and breathable. I would love to own this material and am just waiting for the right top to be released.