I feed a cat that isn't ours. I don't know if the owner neglects her etc. but she always comes to our house hungry. Sometimes I buy cat food but other times when it runs out I get food from the cupboard. My mum gets angry so I told her I didn't feed her our spare meat when I did, is this a really bad sin?
In general, lying is a big deal:
Narrated Anas bin Malik: The Prophet said, "The biggest of Al-Ka`ba'ir (the great sins) are (1) to join others as partners in worship with Allah, (2) to murder a human being, (3) to be undutiful to one's parents (4) and to make a false statement," or said, "to give a false witness."
Sahih al-Bukhari 6871
It's far better to simply tell the truth, even if someone gets mad. Discovering someone making the smallest of lies leads to mistrust ("what else are they lying about?").
Lying is not the kind of behavior that's suitable for one's parents:
And your Lord has decreed that you not worship except Him, and to parents, good treatment. Whether one or both of them reach old age [while] with you, say not to them [so much as], "uff," and do not repel them but speak to them a noble word.
There are some exceptions to lying (when it serves a greater purpose), e.g.:
A liar is not one who tries to bring reconciliation amongst people and speaks good (in order to avert dispute), or he conveys good. Ibn Shihab said he did not hear that exemption was granted in anything what the people speak as lie but in three cases: in battle, for bringing reconciliation amongst persons and the narration of the words of the husband to his wife, and the narration of the words of a wife to her husband (in a twisted form in order to bring reconciliation between them).
Sahih Muslim 2605 a
I'm not qualified to produce fatawa to declare whether or not exceptions apply in the described circumstances. However, the closest related fatwa I found says:
You should have recourse to evasive language, using words by which you mean something but you know the listener understands something else, as a way to avoid lying. If you have no other way but to lie to your father in order to avoid his anger and ward off harm (incurred on him), then there is no harm in that.
This fatwa indicates the described circumstances are possibly an exceptional case.
The description and language in the post suggests you're aware that your mother disapproved of your behavior, yet persisted anyway. This underlying problem seems to have led to lying. A relevant hadith here is:
Anas narrated from the Apostle about the major sins. He (the Holy Prophet) observed: Associating anyone with Allah, disobedience to parents, killing a person and false utterance.
Sahih Muslim 88 a