One switch control two light (one light or both light ON)
Changing the switch itself involves changing the wiring, and depending on how the room is setup and wired (which you may not fully know until you start opening walls) could be quite a fair amount of work. It's also a bit strange to have multiple switches controlling multiple plugs, so it's not really something that would appeal to future owners (and in fact, may be looked at as a negative).

I'd instead skip all that, and go with "smart" bulbs. There are a number of products on the market (specific product recommendations are something we don't do here) depending on what you're looking for. 

Some are simple on/off, some can control bulb color/brightness, and some have "scene" capability (where you press a single button to set all lights to a preset brightness and/or color). 

Bluetooth / Smartphone controlled

There are many that are smartphone-controlled. Personally I think this is of very limited use -- touching a switch on the wall as I leave/enter the room is more convenient than getting my phone out of my pocket, unlocking it, finding the light control app, waiting for it to load, then adjusting the light. 

The benefit is they're very cheap -- there are 100's of "brands" of a couple dozen distinct models available from China.



I do have some of these in my office at work. I use the app to adjust the color every now and then, but mostly I just use the switch on the lamp they're in to turn them on or off (and it's only me that uses them).

Wireless control

There are a lot of bulbs that are controllable via wireless. Some are IR (with a remote that needs line-of-sight), others are RF (no line-of-sight), and you can also get Wifi and Wifi/RF hybrids.

Nice thing about these is you can get a remote switch that can be mounted to the wall, and have multiple switches if you want. You can leave the existing switch in the room controlling overall on/off (though if turned off, you can't turn lights on from the remote), just not use it at all, or replace it with a blank faceplate.

 

Plug-in systems

There are also a number of ways to remotely control power to the lamps, so you use the existing bulbs. 

 

"Smart home" systems

These can range from wireless remote-based products (some of which also have smartphone controls), to actually replacing your existing switch with a keypad. Some of these product lines are quite extensive, offering a mix of plug-in modules, bulbs, controllable outlets, replacement switches/dimmers (which can be controlled remotely as well as control other devices), wall-mount keypads, handheld remotes, motion sensors and smart-phone interfaces. 

These types of systems can be a bit overkill for a single room, but if you ever want to get into full-house automation/control it is a good starting point.