Sure! That sounds like an exciting itinerary. Here are some travel tips for you:

Best Time to Visit:
Delhi, Lucknow, and Chandigarh have a temperate climate throughout the year. Try to avoid the extreme summers (May - June) and the monsoon season (July - August). Winter (October - February) is a great time to visit for its pleasant weather.
Shimla is best visited during the summer (March - July) when the weather is quite pleasant. If you enjoy snow, the winter months of December - February will be perfect.

Route and Accessibility:
Flight connectivity to Delhi, Lucknow, Chandigarh and Shimla is good from across India. Trains and buses are also viable options. From Chandigarh to Shimla, traveling by road could be a good option because of the scenic beauty.

Altitude and Acclimatization:
While Delhi, Lucknow and Chandigarh are plain cities, Shimla is a hill station at an altitude of about 2200m above sea level. Take some time to get acclimatized to the height once you reach Shimla.

Accommodation and Booking:
All these cities offer various types of accommodations as per your budget and requirements. Pre-booking your hotels can prevent last-minute hassles and can also grant you some discounts.

Clothing and Essentials:
For Delhi, Lucknow and Chandigarh pack according to the season of the visit. In Shimla, always carry warm clothing as the temperatures can drop suddenly at night. Don't forget to carry sunblock, hats, and sunglasses for all the cities due to the tropical sun.

Health and Safety:
Always carry a basic medical kit during your travels. Stay hydrated and take care of your belongings in crowded places.

Local Etiquette and Respect:
Respect the local traditions and customs, especially when visiting religious places. Avoid showing excessive affection in public. Indians appreciate modest dressing. Try to learn a few Hindi phrases, as they can be useful in North India.