Total newbie question here about completing a system

 " analog signal from a computer source ".... huh???

Was trying to keep it simple,,,many computers will output an analog signal using internal digital to analog converter (DAC). 

You definitely need a phono amp to use the turntable. Just to get him up and running, you don’t have to spend much, but if you’re looking for the best possible sound quality, you should find out the model of turntable and the cartridge/needle (if it’s functional) and ask for more feedback with a post on the analog page. Include in your question a budget range and you’ll probably get several great suggestions that fit your needs. You’ll get suggestions here but more people with that expertise will see it if you post in that section too.

If the current turntable doesn’t have a working cartridge, the same can be said for that component as the phono amp.

Since digital is likely to be his most used source, a DAC or streaming device with built-in DAC would also be a good investment. A chromecast audio gets him playing cheaply and easily, but there are better sounding options if you/he wants to spend more. Bluetooth receivers are an option but usually have worse sound quality than things that utilize your wireless network.

Lastly, you need cables to connect everything. You might have these already and just not bothered mentioning them. Interconnects from turntable to phono amp, phono amp to preamp, each other source to the preamp, a set from the preamp to the power amp, and speaker cables between the amp and speakers. Just starting out, there’s no need to go crazy here, but don’t forget about them when picking other items or you’ll end up over budget...even budget friendly options add up when buying several sets. Monoprice has good quality, inexpensive cables if you need them. Used cables are also a great option.

I agree with skipping the equalizer...especially for now.

Do you have a budget in mind for the full system?

Much thanks for all...this has given me a good next step in my understanding. I'll circle back with more info on the TT, but in the meantime I'm intrigued by Willemj's suggestion of "the very good and very affordable ODAC"... I'm a little unclear about the model.. Is this it? https://www.amazon.com/FiiO-E10K-Headphone-Amplifier-Black/dp/B00LP3AMC2/ref=sr_1_1?ie=UTF8&qid=1514410871&sr=8-1&keywords=ODAC
And can I assume you simply connect this to a USB port on your computer, then attach cables from line out on this unit to line in on the preamp?

https://www.amazon.com/JDSLABS-ODAC-Digital-Analog-Converter/dp/B00EJ9N8U2/ref=cm_cr_arp_d_product_top?ie=UTF8

The one you linked to looks fine to start with. You'll need a 2.5mm to RCA cable to connect these DACs to the LS2.

The one the OP linked to is not the ODAC but a FIIO. The ODAC is a now legendary design by an anonymous experienced engineer called NWavguy (you can google him and his description of the design process, plus measurement data) who was fed up by expensive snake oil products and designed an affordable usb dac that really is about as good as the best. It is available from different sources and with different cases.See e.g. here: https://www.jdslabs.com/products/46/standalone-odac-rev-b/
The one I bought is from Mayflower and sells for $119: https://mayflowerelectronics.com/odac-rev-b-stand-alone/
It is a basic usb DAC: you connect it to the usb port of the computer, and you connect the output to the line input of the amplifier. You normally do not need any specific drivers on the computer. Output is 2.0 Volt, just like a standard CD player. It takes its electrical power from the usb port, so no further cables are required. And it is a tiny and discreet box, smaller than a cigarette case.