Is it permissible to supplicate with, "My Lord, grant me a record, and in Paradise a dwelling, and in this world a state that the former and latter generations envy me for"?

Supplicating for a house in Paradise is permissible and مطلوب (desirable/demanded) in Islamic law, and it is recommended to ask Allah for Al-Firdaws (the highest level of Paradise). A Muslim is allowed to ask his Lord for whatever permissible worldly pleasures he wishes, and for all his worldly and otherworldly needs, without transgression. As for supplicating for the supplicant's worldly condition to be so good that both predecessors and successors envy him for it, it appears that this falls under transgression in supplication.