Dudhwa National Park, about five hours' drive north, is the closest major tiger reserve to Lucknow and one of the few places in India where you have a reasonable chance of seeing both tiger and rhinoceros in the same trip. Nawabganj Bird Sanctuary, an hour out on the road to Kanpur, is a manageable half-day for birders in winter.
For something nearer, Bara Banki (an hour east) has the small but atmospheric Mahadeva temple and the Dewa Sharif Sufi shrine. Kakori, on the western edge of the city, holds the Kakori Conspiracy memorial commemorating the 1925 train robbery by Indian revolutionaries. None of these are essential, but Lucknow's other major destinations — Agra, Varanasi, Allahabad — are far enough away to need an overnight rather than a day.