The P115 will allow you to play through a computer. Though it doesn't have native MIDI ports it does have a MIDI USB driver which will allow the keyboard to be recognised as a MIDI device in your computer. So start by installing the USB-MIDI driver supplied by Yamaha for your instrument.
Now, as aleeady commented, to play a software instrument in the PC you don't strictly need DAW.
Some software instruments ("soft synths" for short) can operate in standalone mode. In that case you just need to install the software and configure it to use your keyboard as MIDI input. There are some free standalone synths out there, and many commercial ones.
For example sforzando is a free soundfonts player that can run in standalone. Soundfonts is a standardised file format for sample based synthesis and there are literally thousands of free sounfont files (.sfz extension) out there in the web. So a soundfonts standalone player is the simplest way to play many different sounds in the PC using your kb as a controller.
Another possible approach is to use a so called plugin instrument host. Many soft synths support one (or several) types of sw interface(s) that allows them to be called and used in a integrated way with a host program.
In order just to perform (i.e. no recording and no editing of music), a dedicated host program is suficcient, a fully fledged DAW is not required.
The most common plugin interface in use nowadays is the VST standard, so a VST host program is most advisable for this approach.
VSThost is a free and excellent VST host program. So get this program and install it and start looking for VST compatible soft synths. Sforzando also supports VST, so it can be used in this approach too. But there are thousands of free VST compatible synths, just search the Web for "free VST synths" (and welcome to the "yet another VST to play with" syndrome :-)
Now, a DAW is not strictly required, but most DAWs (or all, depending on your definition of DAW) are also hosts for VST and probably some other plugin interfaces.
So just get a plugin soft synth and install so that it is recognised by the DAW (in the simplest case a .DLL file is to be copied to a plugins folder).
In any of the three approaches described, the keyboard has to be configured in the software (standalone synths, VST host or DAW) as a MIDI input device, so don't forget that step.
Just to wrap up, LMMS (which I didn't know and from the description seems to be quite a nice product, so thanks for showing that) advertises VST native support, soundfonts native support and a couple of soft synths integrated in the package. So it's just a matter of following the configuration steps above without the need for any additional software.