Lindström was settled predominantly by Swedish immigrants and their families. As of the census of 2000, there were 3,015 people, 1,225 households, and 855 families residing in the city. The population density was 1,332.1 people per square mile (515.1/km²). There were 1,322 housing units at an average density of 584.1/sq mi (225.9/km²). The racial makeup of the city was 97.61% White, 0.20% African American, 0.36% Native American, 0.50% Asian, 0.56% from other races, and 0.76% from two or more races. Hispanic or Latino of any race were 1.13% of the population. 25.1% were of German, 22.8% Swedish, 12.8% Norwegian, 7.9% French and 6.3% Irish ancestry according to Census 2000. 100.0% spoke English as their first language.
There were 1,225 households out of which 31.1% had children under the age of 18 living with them, 58.4% were married couples living together, 8.2% had a female householder with no husband present, and 30.2% were non-families. 25.7% of all households were made up of individuals and 13.6% had someone living alone who was 65 years of age or older. The average household size was 2.46 and the average family size was 2.95.
In the city the population was spread out with 26.0% under the age of 18, 6.8% from 18 to 24, 26.5% from 25 to 44, 22.5% from 45 to 64, and 18.1% who were 65 years of age or older. The median age was 39 years. For every 100 females there were 95.8 males. For every 100 females age 18 and over, there were 90.7 males.
The median income for a household in the city was $44,980, and the median income for a family was $50,519. Males had a median income of $42,604 versus $28,163 for females. The per capita income for the city was $21,195. About 5.7% of families and 8.0% of the population were below the poverty line, including 8.6% of those under age 18 and 13.9% of those age 65 or over.