By bus
From Kathmandu there are dozens of daily bus services to Nepalgunj. Few of them have quality services. It's a 10-12 hour ride and an overnight bus journey from Pokhara and Bhairahawa. From Lucknow you can take a bus until Bahraich on the Nepalese border and from there there are plenty of local rickshaws available to corss the border. Once you reach Nepalgunj there are many buses to other parts of Nepal.
Remember to perform your journey during day time.
By plane
Direct flight from Kathmandu. 45-55 min. flight, daily 4-6 flights.
By car
You can reach here from Lucknow in India by car. The drive will take approximately 6 hrs. Thought the drive is through a somewhat deserted area with a variety of landscape. You cross the river Karnali, which is called Ghagrah in India. The River Ghaghara has some tea-stalls for a stop over.