The store in the southern Indian city of Chennai was first opened by her great-great-grandfather in 1928.
Over the decades Nalli has become one of India’s best-known brands of saris. The traditional Indian garment for women, saris are lengths of wide fabric which are first wrapped around the waist and then draped over one shoulder.
Lavanya says the brand’s heritage and reputation for selling the finest silk saris are central to its continuing appeal.
And with annual revenues of more than $100m (£76m) across 29 Indian stores, plus outlets in Singapore and California, business remains strong.
Yet as a growing number of Indian women are choosing to wear Western clothing, or less formal Indian garments, Lavanya is using business skills she gained from spending several years away from the family company to introduce new product lines and take the firm into e-commerce.
Nalli is renowned for selling hand-woven silk saris, which are made from the artisan weavers in the Kanchipuram district of the southern Indian state of Tamil Nadu.
These saris are known for their opulence, their fine fabric, vibrant colours and intricate designs, which range from floral and peacock motifs to checks and stripes.
They are popular as special occasion wear for celebrations, festivals and marriages, and the most beautiful are passed on from one generation to the next.
They are also not cheap, with the most intricate examples costing as much as $3,100 (£2,350).
As a child Lavanya says it was impossible for her not to take an interest in both the company and retailing in general, because her father and grandfather would forever discuss business at the dinner table.
“Work and personal life were amazingly integrated,” she says.
Lavanya herself formally joined the business in 2005, when she was 21. She stayed for four years, before deciding that she wanted to leave to learn about different ways of doing things.
So she first went to the prestigious Harvard Business School in the US to get an MBA (master of business administration).
She then worked with business consulting firm McKinsey in Chicago from 2011 to 2013.
Returning to India in 2014, she then spent a year with an online fashion retailer called Myntra, before finally rejoining the family business in 2015.
With all the experience she had gained while she was away, she says her family were happy to let her take the lead at Nalli.
The challenge Lavanya faces is responding to the continuing change in the fashion tastes of Indian women, which is seeing many of them wear saris far less often.
“Saris were the only choice and preference Indian women had for a very long time, and that has changed over the years,” she says.
While saris still dominate on Indian city streets, it doesn’t take long to spot young women in Western casual wear such as jeans, t-shirts and shirts.
They are buying these from shops opened in India by the likes of Sweden’s H&M, and US chain Gap.
Less formal Indian clothing such as kurtis (a stitched long shirt) and salwar kameez (dresses) have also grown in popularity, especially on college campuses and in the workplace.
Amit Gugnani, a fashion expert at Indian management consultancy business Technopak, explains the growing challenge for companies like Nalli.
He says: “Indian fashion consumers have become more experimental and image-conscious.
“A strong and growing economy coupled with better job prospects, higher disposable income and profound impact of media and technology is revolutionising [the] buying behaviour of Indian consumers.
“It is a fairly large challenge to be able to cater to the modern day Indian consumer – it is a fine balance between understanding the consumer and educating them at the same time about the offering your brand has.”
Backing a hunch
While Nalli has no plans to introduce Western-style clothing, under Lavanya’s direction it has launched a range of kurtis and salwar kameez.
The company has also launched a range of more affordable saris, made from cheaper fabrics, such as a blend of polyester and cotton. This has brought prices down to as low as $2.20 per sari, a fraction of the price of the most expensive silk versions.
Lavanya says that while saris remain the “major revenue generator for the company”, Nalli has “adopted the changing preference of consumers”.
While Lavanya has led the development of the company’s website, to enable sales from around the world, she still intends for the business to double its number of physical stores by 2020.
She says her family continues to support her efforts, particularly because she provides detailed business plans.
“Our set-up is very entrepreneurial, which allows us to keep thinking about different ways of doing things,” says Lavanya.
“So whenever I have an inclination or hunch, I find data that validates my hypothesis. This makes me more confident to chase it further, and my family supports it.
“I’m really grateful to be in the position that I am in today. There is a deep sense of pride to be part of a historic brand that my family has built.”