Final answer:
Sir Gawain is required to find the Green Knight only once in the poem 'Sir Gawain and the Green Knight.' The tale's theme of a chivalric quest mirrors similar romantic and gothic imagery found in 'The Lady of Shalott,' including the noble quests and pursuits of characters like Sir Lancelot.
Step-by-step explanation:
In the context of the poem The Lady of Shalott, the question 'How many times does Gawain have to find the Green Knight?' refers to a different Arthurian tale known as Sir Gawain and the Green Knight. In this chivalric romance, Gawain only has to find the Green Knight once to fulfill a pact. The Green Knight challenges any knight to strike him with his own axe, on the condition that the challenger will find him in a year's time to receive a blow in return. Sir Gawain accepts the challenge, beheads the Green Knight, who then picks up his head and tells Gawain to seek him out at the Green Chapel in a year and a day.
This theme of a quest and fulfilling a promise is consistent with the romantic and gothic themes found in the poems presented in the question. For example, in the excepts from The Lady of Shalott, we find imagery of idealized knights, quests, and cursed fates. The references to Sir Lancelot and Camelot also evoke romantic notions of chivalry and courtly love.
A "red-cross knight" typically refers to a knight who bears the symbol of a red cross, commonly associated with the Crusades and the Knights Templar, representing the embodiment of Christian martial prowess and piety.