Table with clustered Index consuming max memory causing low PLE alerts

For one of my server with below configuration i am continuously receiving alerts for low PLE which ranges between 20- 400 and an average of 90-100 in a day:

Server: SQL server 2008R2

Databases : System and 2 user DB's with max size of DB being 54 GB

RAM: 16 GB

Max server system memory: 12.24 GB

Once i got a hint for memory pressure i used RAMMAP to find memory usage and found private process using 13.8 GB indicating a further doubt on lower memory pressure:

I analysed and found that one of the User DB A was using 8 GB RAM as per the blog from Paul Randal:Additionally i analysed for a period of time and saw tempdb using at an avg of 3-4 GB of RAM

Then with further investigation i went and found that in that database A there was a table having a clustered index consuming on average 6-6.5 GB of the memory.( Fragmentation is not an issue as its been checked)

Now from here i am unsure how to proceed? should i go and create the missing indexes or can drop the unused? or there is something else i need to dig in before making any conclusion.

Please suggest!