Let's go a few steps back....
What you want:
...to be able to show only the live jobs (after a find is performed) and have them show up in a pull-down field...
What you have:
... "LiveCompleteBilled" which uses a value list with each option. So all jobs are tagged as one of those three.
So the status of a record can be or 'Live', or 'Complete', or 'Billed', but we only want the records with status 'Live'.
With other words, you want a drop down list with all the record where the value in field "LiveCompleteBilled" is 'Live'.
Correct so far ?
You have 2 tables, one with the jobs and one timeTable.
You want the drop down list with only the live jobs in the timeTable so users can choose a 'live' job from the list.
You make in the timeTable an autoEnter text field, 'liveTag', with the value 'Live'.
This way you will always have the value 'Live' in that field the moment you create a new record.
For the existing record you have to make sure (by hand) that all the records have the value 'Live' in that given field.
Now we are sure all the records in the timeTable will have a field with the value 'Live'.
In the jobtable, only the records where the user made a choice for 'Live' in the "LiveCompleteBilled" field, will have the value 'Live'.
You make a relationship between your timeTable and your jobtable, call it f.i. Jobs, where 'liveTag' = "LiveCompleteBilled".
With other words, when in field "LiveCompleteBilled", in the jobs table, the value is 'Live', this will be equal to the fixed value in the 'liveTag' field in the timeTable.
So your relationship resolve to true.
You want a list of jobs where the "LiveCompleteBilled" value is 'Live'.
The only records from your jobTable where that is true is for the records with 'Live' in the "LiveCompleteBilled" field.
So we need a value list for all the records where that is true, and the only moment when that is true is when 'Live' is in the "LiveCompleteBilled" and you only want to see that in you timeTable.
The only moment when taht is possible is when the relationship between those two table resolve to true.
So your value list needs to be based on....yes your relationship. And only when 'Live' in timeTable = 'Live' in jobTable.
You make a valuelist:
"Use values from field

Specify Field)"
The field based on your relationship, in your jobtable.
Which field ?
The field that holds the values you want to show your user in the drop down list.
And that is ? The field with the name of the jobs.
But you want only the records with the Live jobs, right ?
Well, you will have them, because you only take the records where the relationship resolve to true and those are the records where timeTable::liveTag = jobTable::"LiveCompleteBilled".
Include only related values ?
Try it out. With and without and see the result.
If stuck. Post again.
HTH