What is the ruling on someone who, while praying, supplicated that a specific girl be his righteous wife, then remembered during the supplication his previous intention not to marry her for certain reasons? Does this fall under the ruling of error and forgetfulness, or lying?

Supplication (Du'a) belongs to the category of 'insha' (constructive/performative utterance) not 'khabar' (informative/declarative statement). Therefore, it is not described as truthful or false. Consequently, if the supplicant remembers during their supplication that they do not currently desire the matter being supplicated for, this is not considered a lie and has no ramifications. A Muslim is permitted to supplicate for whatever they wish of the good things of this world and the Hereafter.