You wouldn't need a transistor for a 16*2 LCD screen. The most power hungry bit is the backlight which needn't use more than can safely be supplied through a plain digital pin (with the right resistor). Buy the black on green ones and they don't need a backlight at all. Without the backlight the display and controller will use a milliamp or two total. The serial ones may use more. 'Sensors' could mean anything, most of my sensors use microamps so they wouldn't need a transistor either.
My sensors are DS18B20, it seems I will use them in parasitic power mode, so they will get power from their own pins. So I can safely power 16x2 LCD (controller and backlight) from spare digital pin?
It seems I really can -- it seems an average 16x2 display (I can't get a datasheet for my particular black on green screen from China, so I checked some common models I know) is about 1.5-3mA.