Is there a way I can play the newest version of DF with the current version of the starter pack and do I need to make any changes in order for it to work correctly?
Download the latest version version of Dwarf Fortress from the
Dwarf Fortress homepage. Decompress it and drag it into the root directory of your Lazy Newb Pack folder. Then in the Dwarf Fortress folder, open the /raw/objects/ folder and copy the "reaction_other.txt" to the /LNP/Baselines/df_44_03/raw/objects folder. Then renamed the /LNP/Baselines/df_44_03/ folder to /LNP/Baselines/df_44_04/.
Graphics packs for DF v0.44.03 are compatible with DF v0.44.04, but you might have to update a flag to mark them as compatible. In the folders found within /LNP/Graphics/ folder, you may need to open them an update the manifest.json files in text editors and update their max version to mark them as 0.44.04. If they don't have a max version field or if they have a blank max version field, then you don't have to worry about it.
Since DFHack and TWBT aren't updated yet, you will probably want to use either the "Standard" or "2D" print mode. The differences in these two (if I recall correctly): The "2D" print mode will allow you to use TTF fonts, while the "Standard" print mode will allow you to use "Nearest" scaling instead of "Linear".
If you use SoundSense, you will want to open the /LNP/Utilities/soundsense/configuration.xml in a text editor and update the path to point to match the new DF directory.
Will the current version of therapist work with the latest DF release?
Not until you install an updated memory layout to tell it how to interact with the latest Dwarf Fortress. They are probably still working on mapping out the memory of the latest Dwarf Fortress. We will need to wait for the DFHack and Dwarf Therapist people to publish a memory map before we can use Dwarf Therapist with the latest Dwarf Fortress.