No. For a variety of reasons.
To set the facts in the first instance. You were on a Type 3 flight ORD-PRG with a connection at FRA and thus delay compensation does not begin until after 3 hours (EUR 300) or 4 hours (EUR 600). Your original delay was not attributable to or caused by LH, but rather by the German government. One can theorize all one wants about why immigration was backed up, but air carriers cannot do more than estimate what a given government will do on a given day. Carriers also cannot be responsible for whatever delay the German government chose to impose on this passenger because he had a non-EU passport.
That is the end of LH's obligation.
In this case, LH was not dealing with a misconnecting passenger, but one where it needed to waive its fare rules because it had not caused a delay. If that took more time than the passenger would have prefered, that is a customer service not an EC 261/2004 issue. But, in any event, had he been rebooked on LH 1394 (presuming availability, which we do not know) scheduled to arrive at 1125, but wound up on 1396 scheduled to arrive at 14:05, that is only a 2:40 delay (presuming that the PRG flight met its schedule) and thus no compensation is due in any event.
No matter how one slices this, OP has a complaint against the German government and nothing more.