This lacks in patients with haemophilia A

The correct option is Antihemophilic factor.

Haemophilia A is a genetic bleeding disorder caused by the deficiency or absence of a specific blood clotting factor. Under normal physiological conditions, the coagulation cascade relies on a series of proteins called clotting factors to form a stable blood clot and prevent excessive bleeding after an injury.

The clotting factors are designated by Roman numerals:
- Factor VIII is known as Antihemophilic factor (AHF) or antihemophilic globulin.
- Factor IX is known as Plasma thromboplastin component (PTC) or Christmas factor, the deficiency of which causes Haemophilia B.
- Calcium ions (${\mathrm{Ca}}^{2+}$) function as Factor IV, which is essential for several steps in the coagulation pathway but is not the factor deficient in haemophilia.
- The X chromosome is the sex chromosome that carries the gene for Factor VIII. While the disease is an X-linked recessive disorder and patients have a mutation on their X chromosome, the X chromosome itself is not lacking in these patients; rather, they lack the functional protein product (Factor VIII) encoded by the gene on that chromosome.

Therefore, the specific substance that lacks or is deficient in patients with haemophilia A is Factor VIII, which is biologically referred to as the Antihemophilic factor.