It shouldn't be confusing, especially if you've been studying WMAP results. They show that space is flat. General relativity tells us that space will have curvature depending upon the mass in it. Where you are, space is curved around the earth; when you throw a ball it curves down to the earth's surface because the mass of the earth has curved space towards it. Look up "gravity probe B" for more information on how the earth curves space in its vicinity.

Cosmologically, the net curvature of the universe is determined by the mass it contains. A universe with more than critical mass (omega >1) has a spherical shape, and straight lines go in circles. With omega < 1, straight lines go in hyperbolas, and at omega = 1, straight lines remain straight.

The makeup of the mass is a real problem for cosmology. There is baryonic mass and electromagnetic energy we all are used to seeing. Then there are the (rest)massless particles, like neutrinos. When physicists add the numbers, they are missing 95% of the universe. There seems to be dark mass, so called because it does not respond to electromagnetic energy, that can be detected by its effect on rotating galaxies and galactic clusters. They are all heavier than they look. That gets us up to about 30% of the total. The remaining is a real mystery, and is the omega-sub-lambda you referred to. Its been dubbed "dark energy", but too little is known about it to give it a good name yet.

Don't think that a 70% error in the present understanding of the mass of the universe is an especially big number. In the beginning, mass and space had to be in balance of 1 part in 10E15 for us to even be here. Small errors then, would have been amplified by time, and now we would either be flung apart, or crunched together long ago. There is a distinct probability that there may be a deficit in mass that results in an open, hyperbolic universe, and space will curve away from us in time to come. But that's not my point.

My point is that space does not now, nor has it ever existed independently of the mass it contains. That was an old Newtonian idea, and even Newton's contemporaries were uncomfortable with it. We now know that mass, space, and time came into existence together, and have coexisted since then, all interacting. Einstein's special theory of relativity combined space and time, then the general theory added mass, and gravity.

You can find some good books on this, if you look. I can recommend "Relativity" by Albert Einstein, as his non-technical publication. For the more mathematically inclined, there is "The Meaning of Relativity", by A. E. There are other good books, too, that explain some of the solutions obtained from Einstein's field equations. A few of them are even good reading.