The full daily Panchang for Lucknow: today's tithi, nakshatra, yoga, karana and vara, with sunrise, sunset, Rahu Kaal and Choghadiya in your local time.
The five limbs — tithi, nakshatra, yoga, karana and vara — change at moments fixed by the Moon and Sun, not by the clock, so a tithi can begin mid-afternoon in Lucknow and be reported on a different date by a panchang computed elsewhere. This page resolves all five against Lucknow's local sunrise, which is the reference Vedic tradition uses to name the day.
All of India keeps one clock — IST, pinned to the 82.5°E meridian — across roughly 28° of longitude. Lucknow lies at 80.95°E, so the Sun reaches its highest point here about 6 minutes later than the clock suggests. That puts solar noon in Lucknow roughly 15 minutes earlier than in New Delhi; sunrise moves with it, though latitude shifts sunrise a little further either way as the seasons turn. Rahu Kaal, Choghadiya and every muhurat are carved out of local sunrise and sunset, so a table copied from a Delhi panchang is wrong for Lucknow by about that much.
Lucknow sits at 26.85°N. Daylight here runs to about 13h 41m at its longest and about 10h 19m at its shortest — a swing of roughly 3h 23m across the year. Because the eight daytime Choghadiya periods are made by dividing sunrise-to-sunset into eight equal parts, each period in Lucknow is noticeably longer in summer than in winter. Rahu Kaal, being one-eighth of the day, moves the same way.
Timings are computed for 26.85°N, 80.95°E (Asia/Kolkata) with the Swiss Ephemeris: the day's exact sunrise and sunset first, then Rahu Kaal, the Choghadiya periods and the panchang limbs derived from them. Nothing is approximated from a nearby larger city.
Not if you want it exact. The solar day in Lucknow runs about 15 minutes earlier than in New Delhi, and every Rahu Kaal and Choghadiya boundary shifts with it. For casual purposes the gap is small; for choosing a muhurat it is large enough to matter.
Because it is not a fixed clock time — it is one-eighth of the daylight span, measured from that morning's sunrise. Daylight in Lucknow varies by about 3h 23m across the year, so both the start time and the length of Rahu Kaal move with it.
No. Rahu Kaal, Choghadiya and the panchang are properties of place and date — identical for everyone in Lucknow on a given day. A muhurat chosen against your own chart is a separate question and needs your birth details.