I have the Lenovo g550, which surprisingly (or not) does not have a DVI connection. Is there any point of using a DVI cable and a converter? My logic says no, but I figured I'd better ask. My screen is (if it matters) AOC e2343f.
The answer is: It depends.
If the laptop has a HDMI port and the screen doesn't have a HDMI port then you should be able to get digital output using a HDMI to DVI cable. Same goes for DisplayPort to DVI cable.
If the laptop only has a standard VGA output and screen has VGA input, then in most cases there won't be a reason why to use a DVI converter. The cheap DVI converters work by simply converting VGA to DVI-I, which is basically VGA with DVI cable. This may not work with some screens that expect digital input from DVI. There are also expensive converters which will actually do analogue to digital conversion and provide digital signal at the output and are used with monitors that do not support DVI-I input. With them, there usually won't be any improvement in the picture quality because the source signal is of low quality.
Do note that in my answer I assumed that the VGA cable is not a problem and sometimes it can be. I've heard that in some cases with very long cables there can be picture quality improvements if a VGA to DVI-D converter is used in combination with DVI boosters, but this is usually for cables 10+ meters long.