Did Alex get a frontal lobotomy?

Almost certainly not.

He was 'cured' of his violence by aversion therapy [Ludovico's Technique] & released from prison. Suffering from the after-effects of this, he tries to find a painless suicide method. Due to a series of unfortunate coincidences, he ends up back at the house of F. Alexander, who realises who he is & subjects him to further torture. This leads him to jumping out of the window in a bid to commit suicide.

After he wakes up in hospital he is given a series of tests which prove that his aversion therapy has reverted & he is once more capable of violence.
His last line [in the movie] is "I was cured, all right!"

In the book [which also has an additional chapter Kubrick wasn't aware of when he was making the film, as it was excluded from the US edition] there is an explanation that the doctors "undid the therapy" but as far as I can recall, without further explanation.
In the book, the last chapter starts with him going out with a new gang, back to his old ways - something he certainly wouldn't be doing if lobotomised - but soon tires of the lifestyle & contemplates setting down and raising a family… only to be concerned his children may turn out to be even worse.

Refs, Wikipedia: A Clockwork Orange (film) and A Clockwork Orange (novel)

It's been a long time since I read the book or saw the movie, but an explanation of Alex's 'odd responses' is that they can be seen throughout - he is an inveterate liar; all his responses to authority are evasive at best. He also tends to be more puerile than the actor's age would allow for - Alex in the book is only 15, which makes a little more sense. His internal monologue is often at odds with his external responses. He is his own 'unreliable witness'.

Now we have a clip, I see absolutely nothing wrong with Alex… he's just "being Alex". The reference to the operation might be the movie's way of covering the book's explanation of the treatment being 'undone'.
I see absolutely zero evidence of a lobotomy - though my entire experience of those is from other movies not real life - but they seem to tend towards becoming a drooling vegetable… vis, One Flew Over the Cuckoo's Nest…

No, it wasn't a lobotomy.

Alex's brain has been reprogrammed using the aversion therapy:

Aversion therapy is a form of psychological treatment in which the patient is exposed to a stimulus while simultaneously being subjected to some form of discomfort. This conditioning is intended to cause the patient to associate the stimulus with unpleasant sensations with the intention of quelling the targeted (sometimes compulsive) behavior.

This is a well-known (albeit controversial) method of curing "undesirable" behaviour: from biting nail (by painting them in bad-tasting nail polish), through alcoholism (by providing alcohol together with Disulfiram, which causes painful reaction when ingested with ethanol) to attempts to "cure homosexuality".

In this particular case, he was forced to watch movies depicting violence at the same time he was given a medicine that was making him feel sick. This made him unable to act violently without feeling the same nausea and pain. As the unfortunate side effect of this therapy, he was also reacting in the same way to his beloved classical music, which has pushed him towards suicide.

In the end, the therapy is reversed, but again it is not done via lobotomy, but possibly via a brain surgery. People that have gone through lobotomy behave much different from Alex - they are passive, docile, almost zombified:

The purpose of the operation was to reduce the symptoms of mental disorders, and it was recognized that this was accomplished at the expense of a person's personality and intellect. [...]. Following the operation, spontaneity, responsiveness, self-awareness, and self-control were reduced. The activity was replaced by inertia, and people were left emotionally blunted and restricted in their intellectual range".

Here we can see that while Alex is not a brilliant genius, after an initial confusion, he starts replying quickly in a way typical to himself - talking about sex ("in and out") and violence, and he gets quite excited about it, to the point where he hurts his arm - this wouldn't be a behaviour of a lobotomised person.

Indeed, as @Tetsujin mentioned, there is one more chapter in the book showing Alex a few years later leading a new gang but slowly getting bored with such life.