If you are travelling to Lucknow then to move one place to another the best option is Uber. Its very cheap and comfortable. Since most of rickshaw ply without meter. If you are not good at bargaining go blindly for uber/ola.
I started my first day at Lucknow with british residency. Its was used to be factory and storage house of ammunition of British. Well built and its own aura and beauty. Best for photography and if you seek peaceful day you can spend your morning or evening.
There are two parks nearby where you can just relax. In afternoon you can visit chotta Imambara and Jama mashid. Chota Imambara. For evening you can go to marine drive replica of Mumbai marine drive which is on Gomati river. And have walk into city and feel the nawabee air and have very hood non veg food.
(P.s If you are pure vegetarian then ots very difficult to get good veg restaurant. I would suggest to go to any cafe as there are lot one.
Evening you can visit samaj parivartan sthal another massive marbled area noting exciting hut massive and lightning is mesmerising.