Let's assume the person is 50kg (low estimate), a lethal dose is 150mg * 50 per day, or 7500mg. Three lemonades is merely 2x the point where caffeine intoxication starts, so I'd expect the following symptoms:

According to the DSM-5, caffeine intoxication may be diagnosed if five (or more) of the following symptoms develop after recent consumption of caffeine: restlessness, nervousness, excitement, insomnia, flushed face, diuresis, gastrointestinal disturbance, muscle twitching, rambling flow of thought and speech, tachycardia or cardiac arrhythmia, periods of inexhaustibility, and psychomotor agitation.

And at very high levels of consumption (about 5x of those three lemonades):

According to the International Classification of Diseases (ICD-11), cases of very high caffeine intake (e.g. > 5 g) may result in caffeine intoxication with symptoms including mania, depression, lapses in judgment, disorientation, disinhibition, delusions, hallucinations or psychosis, and rhabdomyolysis.

None of those are life threatening, unless you have an underlying medical condition that makes you especially sensitive to caffeine. So three large lemonades would give you moderate symptoms, and those would likely go away within hours. The person in the article didn't die from caffeine overdose, they died from a heart attack, meaning they likely had significant health issues where the high caffeine load pushed their heart too far. If you'll notice, heart attack isn't one of the symptoms at all, even with a much higher caffeine load.