Not exactly. PIA operate a flight between Delhi and Lahore. About two years ago it cost me £220 return. Flight only takes about 45 minutes. Not sure if they still operate the Mumbai-Karachi flight.

There's also a bus from Delhi to Lahore that about £20 (if I remember correctly). It'll probably take about 10 hours.

If you are not of Indian, Pakistani, Sri Lankan or Bangladeshi origins then visas should not be a problem (apart from the cost). Origin means that neither you, your parents, grandparents or spouse were born in any of these countries or previously held citizenship of any of these countries.