Abbas - Tanwîr al-Miqbâs min Tafsîr Ibn ‘Abbâs
(So eat of the lawful and good food which Allah hath provided for you) of crops and cattle and wholesome things, (and thank) and remember (the bounty of your Lord if it is Him ye serve) if it is really Him you want to worship through the prohibition of some cattle and crops. If you have done so to worship Allah, then make them lawful, for worshipping Allah entails making lawful that which you have made forbidden.
The Command to eat Lawful Provisions and to be Thankful, and an Explanation of what is Unlawful
Allah orders His believing servants to eat the good and lawful things that He has provided, and to give thanks to Him for that, for He is the Giver and Originator of all favors, Who alone deserves to be worshipped, having no partners or associate. Then Allah mentions what He has forbidden things which harm them in both religious and worldly affairs, i.,e., dead meat, blood and the flesh of pigs.
وَمَآ أُهِلَّ لِغَيْرِ اللَّهِ بِهِ
(and any animal which is slaughtered as a sacrifice for other than Allah.) meaning, it was slaughtered with the mention of a name other than that of Allah. Nevertheless,
(But if one is forced by necessity.) meaning, if one needs to do it, without deliberately disobeying or transgressing, then,
فَإِنَّ اللَّهَ غَفُورٌ رَّحِيمٌ
(Allah is Pardoning, Most Merciful.) We have already discussed a similar Ayah in Surat Al-Baqarah, and there is no need to repeat it here. And to Allah be praise. Then Allah forbids us to follow the ways of the idolators who declare things to be permitted or forbidden based upon their own whims and whatever names they agree on, such as the Bahirah (a she-camel whose milk was spared for the idols and nobody was allowed to milk it), the Sa'ibah (a she-camel let loose for free pasture for their false gods, idols, etc., and nothing was allowed to be carried on it), the Wasilah (a she-camel set free for idols because it has given birth to a she-camel at its first delivery and then again gives birth to a she-camel at its second delivery) and the Ham (a stallion camel freed from work for the sake of their idols, after it had finished a number of acts of copulation assigned for it), and so on. All of these were laws and customs that were invented during jahiliyyah. Then Allah says:
(And do not describe what your tongues have lied about, saying: "This is lawful and this is forbidden,'' to invent lies against Allah.) This includes everyone who comes up with an innovation (Bid`ah) for which he has no evidence from the Shari`ah, or whoever declares something lawful that Allah has forbidden, or whoever declares something unlawful that Allah has permitted, only because it suits his opinions or whim to do so.
(describe what...) meaning, do not speak lies because of what your tongues put forth. Then Allah warns against that by saying:
(Verily, those who invent lies against Allah, will never succeed.) meaning, either in this world or the Hereafter. As for this world, it is transient pleasure, and in the Hereafter, theirs will be a severe punishment, as Allah says:
(Verily, those who invent a lie against Allah, will never be successful. (A brief) enjoyment in this world! and then to Us will be their return, then We shall make them taste the severest torment because they disbelieved.) (10:69-70)
Maududi - Sayyid Abul Ala Maududi - Tafhim al-Qur'an
This shows that the above mentioned famine had come to an end at the time of the revelation of this Surah.
Here the observation of the lawful and the unlawful has been made the test of worship of Allah. Those who claim to be the servants of Allah will eat what is lawful and pure and show gratitude to Him and will scrupulously refrain from what is forbidden and impure.
Please refer also to II: 173, V: 3 and VI: 145.
This verse clearly shows that none but Allah has the right to declare a thing to be lawful or unlawful. Or, in other words, the right of making laws exclusively rests with Allah. Therefore, any person, who will dare to decide about the lawful and the unlawful, will transgress his powers. Of course, a person, who acknowledges the Divine law as the final authority, may deduce from it whether a certain thing or action is lawful or unlawful.
The arrogation of the right of determining the lawful and the unlawful has been declared to be a falsehood on Allah for two reasons: (1) Such a person, so to say, claims that what he declares to be lawful or unlawful disregarding the authority of the Divine Book, has been made lawful or unlawful by God or (2) he means to claim that Allah has given up the authority of making lawful and unlawful and has thus left man free to make his own laws for the conduct of life. It is obvious that each of these claims will be a "falsehood" and a false imputation to Allah.