depending on the design of the op amp the drop out of the op amp won't be constant.
For example just because the drop is 1.5V with +/- 15V supplies doesn't mean it will be 1.5V with 0/5V supplies.
The LF347 you mentioned for instance does not have a constant drop out across input voltage options. Theres a graph in the datasheet showing this.
The actual output swing will vary with a few things:
- output current (which can also be presented as output voltage swing vs load resistance)
- input voltage (this can usually be tied into the output current)
- frequency and gain
You have to consider all these in determining your maximum output swing and these numbers are usually defined in the graphs in the datasheet.
When you look for an op amp for a specific purpose you can get away with generic op amps but you will find better performance in parts designed for the task at hand. The op amp designers usually attempt to mitigate some the variations i've listed above for particular applications.
For instance usually rail to rail op amps can drive the output to the rails when the output is open circuit but you will still find they will not drive all the way to the rails when driving a real load and could be substantially under the rails if a large amount of current relative to their rating is sourced/sunk. Additionally rail to rail op amps usually have low drive capabilities.