You can create something like the following. You can also adjust the IOR to your liking; this is just a sample at 1.2.
Result with Shady Puck in the background:
Mesh sideview profile:
Start by keying Shift + A and going to Mesh > Sphere. Key R, then X, then 90. Key Numpad 3 and Numpad 5 to enter Right Orthographic view. Key Tab and Z to enter Edit Mode and Wireframe View, respectively. Key B for Box Select and drag while holding down your LMB to select the following vertices.
Key S, then Y, then .3 to scale the selected vertices down to a more lens-like shape. Key G, then Y, then .48 to slide them over. You now have half a double convex lens. You should see something like the following.
Key A once or twice to deselect all vertices. Key B for Box Select and drag while holding down your LMB to select the following vertices.
Key X and choose Vertices. Tab out of Edit Mode and key Z to exit Wireframe View. Go to the Properties panel > Object modifiers tab and add a Mirror modifier. Make sure Z is checked under Axis: and nothing else. Your settings should look like the following.
Add a Subdivision surface modifier. Set the View: value to 3 and the Render: value to 4.
Key T to toggle open/close the Toolshelf. Go to Tools tab > Edit dropdown > Shading: and select Smooth.
You are now done with modeling.
This is where the magic happens. Go to the Properties panel > Materials tab and add a Glass BSDF shader. Note that you will have to be in Cycles Render for this to work. Play with the IOR: as you wont.
You now have a fully completed double convex lens.
Many of the techniques from this piece are gathered from tutor4u's awesome Focused Text Animation tutorial.
The following is the .blend file with the lens and Shady Puck text from the first image.