As you have asked about the vacancy or recruitment in Liquid Propulsion Systems Centre of Indian Space research Organization (ISRO), I am giving you information about it, check below for the details
I want to tell you that currently there is no recruitment going on in it.
However, you can check its website regularly to know about it.

To check it
Go to LPSC website
Click on recruitment in the left side of screen, the page open look like




Here, you will find the information about the recruitment.

Here I found following:
Recruitment for the posts of Technical Assistant, Technician-'B' and Draughtsman-'B' - Online submission of applications is closed.

Results of Previous Recruitment
1. Result of recruitment of Technician 'B' Fitter [UR, OBC, SC, ST & PH]
2. Result of recruitment of Technician 'B' Electrician [UR]
3. Result of recruitment of Technician 'B' Turner [UR & ST]
4. Result of recruitment of Technician 'B' Plumber [UR]