Is this a gardening question or a math question?
 
Gardening says put down weed stop fabric and put 3-inches of mulch (lava rock can be used for mulch) on top.  One cubic foot of lava rock would cover 4-square feet.
 
If it's a math question, the answer is more fun.  Mathematics is all about how much.  In this case there is one.  How ever you divide it up, it is still one.  Unless we change the units of measure.  Cubic feet is a measure of volume.  Let's stick with cubic feet.
 
One cubic foot is one foot wide, one foot long and one foot deep.  The length x width x depth must equal one. 
1 x1  x 1  = 1
or
1 x 2 x ½ = 1
or
2 x 2 x ¼ = 1
 
etc.
 
Square feet is a different unit of measure.  It is area instead of volume.  Area is related to volume by the depth, or thickness.  Every real thing has thickness but when we talk about area (square feet) we are only talking about the surface.  We ignore the third dimension or pretend it has no thickness.  So to answer the question:
 
How Many Feet Will 1 CU Feet Of Lava Rock Cover?
 
It depends on the thickness of the real thing.  We have to stop ignoring the thickness and talk about the volume.  The volume won't change.  there will be a length and a width and a depth.  The volume will be one cubic foot.
 
If you spread it 6-inches deep (½-foot), you can use one cubic foot to cover 1-foot wide and one foot long, twice.  That would be two square feet, ½-foot deep.
 
If you put it 3-inches deep (¼-foot) you can cover 1-foot wide, one foot long four times.  That would be 4-square feet, ¼-foot deep.
 
2-inch =  1/6 foot, so 1 cubic foot will cover 6 square feet if it is 1/6-foot deep. 
 
If you put it one inch deep (small rocks, 1/12-foot) you can cover 12-square feet.
 
I hope this was as fun for you as it was for me.

 Lava rock is lighter in weight than most gravels so it has a bit more volume per ton than crushed limestone, granite etc.  For calculating lava rock volume: 1 ton (2000 lbs) = slightly more than a cubic yard (27 cubic feet).
 
My rule of thumb for ordering bulk or bagged lava rock: 
 
1 cubic foot of lava rock will cover apx 5.5 to 6.0 sq feet 2" thick.
 
A ton of 1/2" to 3/4" sized lava rock will cover apx 160 to 180 square feet @ 2" thick. (Or 60 to 100 square feet @ 4" thick and so on)
 
I suggest weed fabric (NOT plastic) be installed prior to spreading the gravel.  COSTCO has a great price of the 4' wide x 200 feet long rolls.  Overlap the swans by 3 or 4 inches and use the stakes provided or 60 D sized nails to help hold it in place while you spread the gravel.