Will a Power Conditioner Help?

It may but the only way you can tell is to try one. What you are connecting sounds pretty modest - I would not worry about the load but an APC H15 may do the trick and tell you want current it is drawing.

Serus,

As a former LC-1800 owner, I have to vote against it. The voltage regulation is accomplished by switching transformer taps in 12 volt steps. What this meant was that, for example, if my line voltage of 120 volts went up to 122 volts, the LC-1800 put out 110 volts. I vote no on this one, especially if (like me) you own tube amps without regulated power supplies.
Not only is it a poor design in that regard, but it also doesn't sound very good in my opinion.

the big furman units ref 15 or 20IT are great for all --least expensive for front end stuff is powervar

Alrau1, thanks for adding details about mode of operation of the LC-1800. What I like about it (and many similar units) is the noise rejection by means of a toroidal transformer. It works wonders for digital!
You'll also notice that I specifically said to NOT connect a power amplifier through this gadget. It does limit current which is an issue with high power units.
I guess I don't encounter large voltage fluctuations, so I haven't noticed erratic behavior. Like I said, there are other units and i'm sure that some of these do not switch taps but just filter the noise through a magnetic circuit. These are much more effective than some pathetic implementations with lots of LEDs and a digital display on the front panel...

Serus,

Just one correction: unless Tripplite redesigned the LC-1800 since I bought mine over 10 years ago, the tranny is NOT toroidal. It is a true transformer, with separate primary and secondary windings, though, not an autoformer (a single winding and no isolation).