Final answer:
The texts of Arthurian romance do not clearly state that the lady of the castle was in love with Sir Gawain, suggesting that any admiration for Gawain was more platonic and tied to his chivalrous deeds rather than romantic love.
Step-by-step explanation:
The question appears to be referencing the complex relationships and themes of love found within the tales of King Arthur and the Knights of the Round Table.
Regarding the specific case of whether the lady of the castle was in love with Sir Gawain, there is no clear indication within the classic texts, such as Sir Thomas Malory's Le Morte d'Arthur or the anonymous Pearl Poet's Sir Gawain and the Green Knight, that she was romantically in love with him.
In the context of Arthurian romance, including the tale of The Lady of Shalott, relationships were often idealized and dedicatedly platonic.
The love Gawain may have inspired was more likely admiration for his chivalrous deeds and virtue rather than a consummated romantic love.