Residential property in Alambagh is a bad idea as suggested by the above member. It is an outright commercial area and unless you have a commercial establishment nearby and cannot travel due to some issues, I would suggest you to stay away from Alambagh. You can however look at Chowki which is also a commercial hub but it offers a mixture of residential and commercial establishments. The prices in Chowki as of today offer value for money deals and I expect the prices to increase over a period of time say between 7 to 10 years. Think medium to long term for any investment in parts of old Lucknow or close by areas.
Alambagh is primarily a commercial sector located in the Cis Gomti zone 5 region, most parts adjoining old Lucknow are saturated with not much scope for future construction or much financial appreciation over short to medium term. The only rocking sector in this area is the Hardoi Road because of its new construction, open spaces and close proximity to the Indian Institute of Management (IIM) offering good rentals. You can check out projects in Hardoi Road or neighboring Chowk which is a mixture of residential and commercial segments. As far as Alambagh is concerned I have not seen much residential real estate activity in the region for a long time.