There could be two sources of this misinformation.
- Confusion of the words lime (a citrus family fruit) and lime-water (a highly alkaline corrosive solution of calcium hydroxide).
The name lime for the citrus fruit originally comes from Arabic and it does have many cognates in South Asian languages. The lime of calcium hydroxide is connected to German and Latin! Orthogonal meanings and origins.
- Second source of confusion could be citrate salts or buffers. Citrate salts of sodium or potassium are indeed mildly alkaline.
In short, drinking lemon juice will not increase alkalinity, it may cause acidity instead and may cause pain in stomach ulcers if there are any. Citrate salts are traditionally used in antacid formulations where citric acid and sodium bicarbonate powder is mixed with water as an antacid. Nature has a very good system of controlling internal pH.