Poles borrowed the original Latin alphabet of the Czechs.
No, they borrowed it from the ancient Romans as did almost anyone else in Europe.
Afterwards, the Czechs Germanized their alphabet, while the Poles have refused to do so.
The Czechs didn't do that. They rather "Husitited" it as the Czech diacritical marks were originally invented by Jan Hus, the great Czech reformer. So the Czechs "czechised" the Latin alphabet so to speak.
Lithuania decided to change to the modern Czech alphabet to distinguish themselves from Poland
That's disputable. The Czech invention had one big advantage which would make people feel inclined to adopt it: you only have to use one symbol rather than two for rendering a single sound. But the Lithuanian alphabet has Polish letters in it, too.