Hey There Chad,
There are a couple of answers to your question so allow me to break them down for you a little and they really depend on what smart hardware you choose to use…
The first thing you could choose to use would be a smart bulb. This would allow you to remotely control the lamp providing power was supplied to the bulb. Assuming power is supplied, you could remotely turn it on or off, and include it in automations.
The problem comes with the use of the physical switch on the lamp that you mention; when this switch is off, power is cut off to the bulb and thus you wouldn’t be able to control it, say to turn it back on. The switch on the lamp in essence breaks the power connection to the bulb and as such no power means no smart functionality. In order to control the bulb again, you would need to physically turn the switch on after which you could control it.
The next option you have is a smart receptacle where you can control the power at the socket. This option however, like the bulb breaks down when you physically turn off the lamp as no power gets to the bulb regardless of the state of the receptical.
What I did to solve this problem in my bedroom was to install switches above by bedside receptacles within the wall but installed just above my bedside tables; so they’re physical wall switches but switch the top receptacle which the lamps are plugged into. I then use smart dimmer switches and disable (break) the physical switch on the lamp. So basically the lamps are controlled by the smart switches in the wall which can always be controlled both virtually and physically.
I’m not a lover of smart bulbs - I installed a load of Hue bulbs but removed them all because of the lack of switches available and I like the ability to use both an app (or automation) or physical switches. For most of my “lamps” that are plugged into receptacles I’ve ended up putting a switch about 3ft above the receptacle and switching the top receptacle.
Hope this helps but shout if you need more explanation.