Is it two isomers with at least one stereogenic center each but the corresponding center on the other isomer will rotate the plane of polarized light in the opposite direction. Is this applicable to meso compounds which aren't chiral overall but have stereogenic centers?
d- l- Nomenclature as well as (+), (-) refer to a physical property of the molecule, its optical rotation. Optical rotation is a result of chirality, a topological property of the molecule. So d-, l- is something that you can generally measure with a polarimeter. If you have a 1:1 mixture of the 2 enantiomers then you will see zero rotation and this mixture is called racemic and named with the dl- prefix. A meso compound also has zero optical rotation since it is achiral but as it is not a (racemic) mixture the dl- notation doesn't make sense but you might see it used sometimes.
The problem now is if you are given a pair of enantiomeric molecules that are mirror images how do you name them so you can tell them apart every time? This is why the D-, L- and R-, S- notations were introduced. D- L- is the older and more naive approach that was later improved by the R-, S- (CIP) notation. Unfortunately as chemistry is a science with long history that is also used by other non chemistry-trained professionals, several times older naming conventions have survived. So you have to know all of them!
So very simply, d-, l- reflect a real physical property of the molecule and D-, L- (and R-, S-) is a way to distinguish between molecules that contain stereogenic centres (and might be or not be chiral). Actually even the R-, S- system has been criticized for not being rigorous enough. I saw a paper where a new naming system was suggested but it is not possible to read this without knowledge of advanced maths (group theory, algebraic topology)
The d- and l- nomenclature is exactly the same as the (+)- and (-)- nomenclature. It is used to indicate the optical rotation of enantiomers. As such it is not applicable to meso- compounds (or diastereomers in general), because it is not unambiguous.
Diastereomers still have chiral centers, and as such they exhibit optical rotation, but it is absolutely useless to specify the direction of it in the name.
Note that the d- and l- nomenclature is discouraged by IUPAC. (+)- and (-)- prefixes should be used, so as to minimize confusion with the D- and L- nomenclature.