With a rank of 7900 and armed forces rank of 229 (I belong to the general category), is there any chance of getting core branch at IET Lucknow?

Admission to IET Lucknow can be done through the UPSEE exam. If you belong to the general category then you should definitely put some effort into it. 

With a rank of 7900 and armed forces rank of 229 while belonging to the general category can be difficult for admission. There is no chance that you will be picked in the first few rounds and get the best branches. Your rank might be called by the 4th or the 5th round if there are still seats available.

The detailed analysis for 4th round counseling with the rank and specific branches are as follows: -

Around the rank 7000, the 5th round of counseling begins and by then all of these above-mentioned branches are already filled or have very few vacancies. 

New core branches such as Electrical and Instrumentation Engineering are introduced and candidates with a rank near about 7000 are admitted into it. 

The above-mentioned analysis is for general category students only and it huge varies for any other category