Question: When are the Lyrans allowed to attack the Federation?

Answer: As per rule (602.14), the Lyrans are not allowed to operate in Federation space (i.e., invade the Federation) during Turns #7-#9, except for an expeditionary fleet. While nothing else is explicitly stated, it's clear that the intention is that the Lyrans cannot attack the Federation prior to Turn #7.

Question: When are the Lyrans allowed to attack the Tholians?

Answer: Rule (603.0) allows the Lyrans to operate in the territory of any empire that is in the war. They can never "start a war" with the Tholians on their own. The Klingons can attack the Tholians on Turn #7 or later (602.11) but the Lyrans are only allowed to operate in "Klingon, Kzinti, Lyran, and Hydran" territory (plus an expeditionary fleet in Federation space) during Turns #7 through #9, so the earliest that the Lyrans can participate in attacks on the Tholians is Turn #10, and then only if the Klingons have already started a war with the Tholians.

Question: On Turn #1 of the General War, may the Lyrans use Retrograde Movement to Klingon bases and, in doing so, accept internment?

Answer: Nice try. Rules (503.61) and (601.161) both specifically mention the prohibition against Lyrans entering Klingon territory on Turn #1. No exception is given for this phony internment.