The thirteen years between the end of LOCH and ROCH, and the first four years of ROCH, depicted a period of uneasy...I wouldn't call it peace, exactly, but a temporary cessation of hostilities between the Mongol Empire and the Southern Sung Kingdom.
Genghis Khan died at the end of LOCH. With his death, the unified Mongol Empire began a long process of splintering into separate factions. True to the promise that they made to their dying father, the sons of Genghis did not engage in open military conflict against each other, but the lack of further action against the Southern Sung after the defeat of the Juchen Jin Empire for seventeen or eighteen years after the death Genghis Khan suggests some reconsidered priorities within the Mongol Empire.
In history, the Mongols seemed to temporarily lose interest in China even during Genghis Khan's final years. The Mongols had already destroyed the Hsi Hsia Kingdom and had the Jin Empire on its heels. In Genghis' last campaigns, however, he seemed more interested in Central Asia, the Middle East, and Eastern Europe than China. Indeed, the Mongol invasion was focused westward at the time of and for some years after Genghis' death. The Jin Empire would not be eradicated until seven years of Genghis' passing, and the Southern Sung would not fall until Genghis' grandson Kublai was a middle-aged man in C.E. 1279.
Gwok Jing, the staunch defender of the Southern Sung Kingdom, felt certain enough after Genghis' death that there would be no more immediate confrontations between the Mongols and the Sung that he was willing to leave the Central Plains with Wong Yung and spend the next thirteen years away from the mainland on Peach Blossom Island. When the Gwoks did return thirteen years after the end of LOCH, it was for personal rather than military reasons. When Gwok Jing brought young Yeung Gor to Mt. Chung Nam a year or so later, they had to enter Mongol-controlled territory (Mt. Chung Nam is in northern China, which had been ruled by the Jin Empire for many decades before falling under Mongol control). Gwok Jing took the precaution of dressing himself and Yeung Gor inconspicuously to avoid trouble, but they did not encounter scenes of mass slaughter of Chinese civilians by Mongol troops...nor did Gwok Jing feel compelled to learn of any Mongol military activity in the area while he was there. This suggests that there was no immediate threat of Mongol invasion during the first four years of ROCH, although that would change rapidly after the Golden Wheel Monk arrived in China to reconniter and possibly gain control of Chinese wulin through subterfuge.
In sum, seventeen or eighteen years passed between the death of Genghis Khan and the beginning of Kublai's assaults of Seung Yeung in which the Mongols and Sung did little but eye each other warily across their borders, the Mongols preparing to invade and the Sung preparing to defend, but neither side overly eager to re-engage the conflict that had started nearly twenty years earlier.