L : language, obviously checked by IRCC.
P : physical presence, also checked by IRCC, with the help of the entry/exit report send by CBSA.
P : prohibitions, validated by IRCC once L, P and background checks are done. It's just that people usually say LPP because for most, BC is done quickly and LP comes later, so L and P are the last checks for the seconds P and it comes with them.
Also, background checks contain both criminality checks done by RCMP and security checks done by CBSA and mostly CSIS, and its the one who, if needed by IRCC, will potentially take ages... :/