KA101 the Pennsylvania Lawyer here.
Generally, escaped prisoners aren't even tried for escaping prison, simply sent back. Extra sentences would be "$SENTENCE, to be served consecutively" to tack it onto the previous term, or as a potential Leniency "$SENTENCE, to be served concurrently" to have it run at the same time. (So, you could be doing (say) 3 years for Theft and another 5 for Assault. That would be 8 years consecutive, or 5 years concurrent.)
For those of us outside the US, our "federal" system means that different cities might mean significantly separate justice systems: in particular, most crimes are actually prosecuted by the individual state where they took place, rather than the DC government. So Liberals in LA would likely be arrested by California, not by the Government. (Until you do something like Treason or pull a crime on the Army Base, which is federal property so the feds handle it. The Nuclear Plant is in fact NOT federal property, IIRC, so it wouldn't count.) Each state runs their own police, courts, and prisons, as does the DC crowd. (Federal facilities are heavier-duty and usually harsher.) And then there's the problem of the LCS as a multi-state "domestic terror network" so the FBI starts coordinating multiple states' investigations. Cue "FBI HUNTS LCS" and inevitable destruction.
Upshot: In National LCS, your sleeper Lawyer in a given area might be able to tie up the process for a few days via the extradition paperwork, so you could have (say) 2-3 days to spring the Liberal from the Police Station.
Example: Flighty the Liberal jailed in NY, escapes, arrested in LA on escaped-fugitive charge. LA lawyer can buy the LA squads three days to break Flighty back out, but SEA/NY couldn't as they aren't admitted to practice in California. If Flighty had done anything criminal in LA, California would possibly want to try xyr for that. Who gets Flighty at the end of the trial depends on the crimes involved and the trial results.
I figure the three months is supposed to represent a mandatory wait while the wheels of bureaucracy turn and the Conservatives execute all the prisoners ahead of your guy in the execution queue, and thus cannot really be hurried. At C+ death penalty, I could see the liberal getting summarily executed with no wait (or even a trial), but otherwise I think it should reset the death row counter back to three months. Maybe there should also be a chance to get the death sentence downgraded to imprisonment if the laws have become more liberal in the meantime. At L+, the death penalty is obviously abolished, and I think the game is already supposed to cancel pending executions when that happens.
As for escaping prison always resulting in a life sentence, I think that was mainly a hack to keep people from completely cleaning their criminal records by escaping prison and then lawyering themselves free of the escape charge. Since that is no longer an issue, it should probably be toned down. I don't think escaping prison is a crime at all in some jurisdictions, provided you don't break any other laws while breaking out.
Yeah, non-C+ DP does take forever to process.
That last bit seems completely counterintuitive and I can't imagine any jurisdiction failing to make escaping from lawful confinement (as in, jail/prison) a crime. Gonna ask for a cite there.