service mongod cant start, permission denied mongod.lock when changing dbpath
If you now command:

sudo chown -R mongodb:mongodb  /home/user/mongodb
sudo service mongod restart


It will work!

Problems here was that you gave command sudo mongod --dbpath /home/user/mongodb/data/ what created ROOT ownded files to that /home/user/mongodb/data/ directory and your "normal" mongodb user don't have right to overwrite those.

So, NEVER start your mongod as root OR if you do so, remember reset ownership of those data files back to mongodb.