The chain is composed of multiple instances of only 2 possible elements:
LT and LLT. Reasoning:
You can't have LLL, else the Liar's statement would be truth
You can't have TT, else the Truther's statement would be false
These elements both have one truther in them, and one is of length 2 and another is of length 3.
Thus, the question becomes: "How many addends of either 2 or 3 can an addition have to sum to N? "
The only answer for N=7 is exactly three: 2+2+3
Three Friends
Three is the maximum number of Friends. Each Friend must be between two Foes. There is no way to place 4 people in a circle of seven where none of them are adjacent. You can place 3 people without adjacencies, so the maximum number of Friends is three. Three is also the minimum number of Friends. Each Foe must be adjacent to at least 1 Friend, and if two friends are placed as far apart as possible, there will be two Foes between them on one side, and three on the other. The middle of the three Foes is not adjacent to any Friends. So there must be at minimum three Friends. Since there must be at minimum three Friends, and at maximum three Friends, there are three Friends. Maybe d'Artagnan should see if they're recruiting?