Let's see the context:
New International Version
1 The Levitical priests—indeed, the whole tribe of Levi—are to have no allotment or inheritance with Israel. They shall live on the food offerings presented to the Lord, for that is their inheritance. 2They shall have no inheritance among their fellow Israelites; the Lord is their inheritance, as he promised them.
3 This is the share due the priests from the people who sacrifice a bull or a sheep: the shoulder, the internal organs and the meat from the head. 4You are to give them the firstfruits of your grain, new wine and olive oil, and the first wool from the shearing of your sheep, 5for the Lord your God has chosen them and their descendants out of all your tribes to stand and minister in the Lord’s name always.
There is no mention of the kinds of festivals or the kinds of offerings: 1. Burnt Offering 2. Grain Offering 3. Peace Offering 4. Sin Offering or 5. Guilt Offering.
https://www.gotquestions.org/Old-Testament-sacrifices.html (pointed out by Tiago in his comment)
Each of these sacrifices involved certain elements, either animal or fruit of the field, and had a specific purpose. Most were split into two or three portions—God’s portion, the portion for the Levites or priests, and, if there was a third, a portion kept by the person offering the sacrifice. The sacrifices can be broadly categorized as either voluntary or mandatory offerings.
Deuteronomy 18 is a general description so that the sons of Levi have a summary understanding of roughly what belongs to them. It describes the case where the priests and Levites' share of the offering.
Deuteronomy 12 describes the case where the family ate a share of their offering:
4 You must not worship the Lord your God in their way. 5But you are to seek the place the Lord your God will choose from among all your tribes to put his Name there for his dwelling. To that place you must go; 6there bring your burnt offerings and sacrifices, your tithes and special gifts, what you have vowed to give and your freewill offerings, and the firstborn of your herds and flocks. 7 There, in the presence of the Lord your God, you and your families shall eat and shall rejoice in everything you have put your hand to, because the Lord your God has blessed you.
In both cases, the offerings were first entirely given to the Lord to be sanctified. They were holy food.
He may eat the most holy food of his God, as well as the holy food;
Are the "Lord's offerings" the one's given during sacrifice and offerings?
Yes, they were set apart and sanctified first before consumption.
New International Version
The Levitical priests--indeed, the whole tribe of Levi--are to have no allotment or inheritance with Israel. They shall live on the food offerings presented to the LORD, for that is their inheritance.
The detail of who can eat what and when is described separately in Leviticus 7.