Why did the fleet support Almeida's revenge?

Was avenging Lourenço de Almeida regarded as a point of honor?

Partly, but the stronger bond came from Lourenço dying to save the other crews, whose sense of debt reinforced loyalty to his father.

Honor mattered, but the fleet's motivation came mainly from Lourenço's conduct at Chaul. Most of the squadron escaped because his ship covered its withdrawal, and survivors returned believing that he had died to save them. Their existing loyalty to Francisco de Almeida was reinforced by a personal debt to his son. Albuquerque heard the circumstances, left Almeida in command, and contributed his own ships and men instead of enforcing the disputed succession.