Qixue 泣血 is a fixed expression used in several ancient texts: ‘weep tears of blood’. In the Lun Heng 論衡 we read:
At the time of the Kings Li and Wu, Pien Ho presented them with a jade-stone, and had his two feet cut off. Offering his stone he wept, till his tears ran dry, when he went on weeping blood. Can the sincerity of Tsou Yen bear a comparison with Pien Ho’s sufferings, or his unjust arrest with the amputation of the feet? Can the sighs towards heaven be put on a parallel with tears of blood?
(tr, A. Forke, p. 113)
From this context we learn that qixue means to cry until the tears are tried up and you continue to cry blood.
Liang 漣: flowing, streaming. Like in the Shijing 詩經 :
I ascended that ruinous wall,
To look towards Fuguan;
And when I saw [you] not [coming from] it;
My tears flowed in streams.
(tr. James Legge)
Shedding bloody tears in streams.