Deuteronomy 12:15
Notwithstanding thou mayest kill and eat flesh in all thy gates, whatsoever thy soul lusteth after, according to the blessing of the LORD thy God which he hath given thee: the unclean and the clean may eat thereof, as of the roebuck, and as of the hart.
The verse allows slaughter for ordinary meals in towns and at home instead of only at the place chosen for worship and sacrifice, identified with Jerusalem as the capital, because once settled throughout Canaan the people could not bring all such slaughter to the place of worship. Domestic animals previously reserved for sanctuary use could now be eaten as common food, just as wild game was eaten, namely the roebuck and the hart, that is gazelles and deer. The meat could be eaten according to the eater's desire and according to the blessing of the Lord, meaning whatever the person desired to eat.
The broad term whatsoever does not make every animal lawful food, but is limited to the kinds God permitted, as defined by the food instructions in Deuteronomy 14 rehearsing Leviticus 11, where unclean animals were specifically forbidden. The unclean and the clean are the people eating, not the animals eaten: both ceremonially clean and unclean persons may eat the permitted ordinary meat, including Israelites and strangers and those temporarily made unclean by rites or contact with unclean things who were barred from sacred meats. The continuing distinction between clean and unclean meats is confirmed by Deuteronomy 14.
Soul in the verse means the person or physical self with appetite and desire for food, so that whatsoever the soul lusts after means whatever the person desires to eat. The soul can therefore hunger and have bodily appetites, rather than being an immortal, intangible essence. The permission reflects what God allowed Israel at that time rather than His unchanging purpose, with its appetite-driven craving presented as evidence that they did not fulfill His better design for them. Deuteronomy 12 belongs to the Levitical law given to the children of Israel, distinguished from the enduring law of God, and as such was abolished by Christ. People may therefore kill and eat flesh freely, including roast lamb and whatever they desire, even at an untimely hour in the night to close a prolonged fast.