Is LP distortion the record or the cartridge?

Yes , the Lyra stylus cleaner is excellent and they supply it with a great brush. It is a bit pricey but IMHO worth it. Many styli are held on only by a gob of glue. Many solvents will attack the glue and then I think you know what happens. The Lyra cleaner will not attack the glue.

mglik has already discovered that his problem is worn records. Old records that distort like that are usually very dirty. So if you are going to play old or used records cleaning them thoroughly is crucial to the life of your stylus. I would play them with a less expensive cartridge that has a replaceable stylus Like a MM Audio Technica. I will not buy used records for this reason. I have seen enough to know you do not want to trust anyone else's record hygiene. 

@mglik , What speakers are you using?
There are certainly times when the reissues are better than the original particularly when it comes to older popular music. The quality of the pressings was not near that of classical music and in the late 50's and 60's recording engineers doing popular music were not as experienced. As an example the early masters of Zappa's first 4 or five discs were terrible. The remasters are fabulous. The reissue of Weather Report's Sweetnighter is significantly superior to the original. I would rather have a good clean pressing at 9/10ths sound than a scratchy one at 10/10ths.

@lewm , for certain. He can add some mass. Soundsmith makes a nice set of graduated cartridge screws. It certainly is not the Atma-Sphere overloading. I have a sneaking suspicion it is just worn records. 
The Lyra Atlas is a fine cartridge certainly in the upper echelon of cartridges. Not the best value but hey, if you have the money why not?
@mglik , what are you using for loudspeakers?

Yes, the Atlas is a great cartridge. You either have a tracking problem or  a worn record problem. Miss-tracking can really chew up vinyl.
On a record you know has the problem try increasing the VTF to max and add a little antiskating. If it sails through without distortion then it is a tracking problem and the Atlas in a Tri Planar will fix it. If you hear the same distortion than you most likely have a worn record problem. Clipping phono stages can also do this but I have a hard time believing the Shalabi would do that. What phono stage are you using?