No, mast height is an important part of the design of the boat itself.  You don't want to accidentally overload the mast partners and base. 

As a general rule, lazy jacks go 2/3rds of the way up the mast (for sloops).  Lug rigs might require you to go higher, but the additional yard helps. 

Maybe do a quick Google image search and look at the scale of what others have done with their lug rigs.

Have a look at this video:

https://youtu.be/KQqxOofndjs

...of a Gig Harbor fiberglass SCAMP.  The balanced lugsail is rigged with lazyjacks (which also act as topping lifts the way they've rigged it here).  As you can see, the lazyjacks appear to be rigged from points (port and starboard) just above or below the halyard, hard to tell exactly which in this video.  The point is, there's no need for a taller mast.  Even with a gaff sail, which already has a taller mast on account of needing more hoist for the peak halyard, the upper ends of the lazyjacks wouldn't be located very far above the upper range of the gaff saddle.

The point here is that there's no need for a taller mast; all you'd need to do is rig the upper ends of the lazyjacks somewhere above where the yard bears against the mast when fully hoisted.  You'd also want to rig some sort of parrel on the boom to keep the whole business level once the halyard is slacked off.  A parrel on the yard might also be needed to keep it from kiting off and getting the heel of the yard fouled outside the lazyjacks, hard to tell.

The real question here is whether you really want lazyjacks at all.  What boat are you thinking of here?  I have a Passagemaker Dinghy with the lug rig, and I do not feel like her 62 square foot sail would benefit from the added complication.  In fact, it would probably make the sail handling more difficult, which is, it is child's play to set or strike the sail once one has the hang of doing it quickly.

.....Michael

I played with Lazy Jacks on the Lug sail for my NE Dory.  I’m so far from an expert it’s downright scary, but I didn’t find them helpful. I ran the extra line through a fairlead set on the very top of my mast. The Lazy Jacks to me just got in the way. If I need to reef I just drop the sail down into the boat and reef the sucker.  Most of the time I have reefed before I even leave the dock.    

The lazyjacks on my Faering Cruiser are extremely convenient, especially when dropping the sails while out on the water. They also keep the boom out of the way while rowing.

Laszlo

Oh, yes, Laszlo is right...I should have thought of the Faering Cruiser as a perfect example of simple lazyjacks for a balanced lug--and one where, I've no doubt, they are absolutely necessary.  With a sail that big (125 sq. ft. vs. PMD's 62) and with spars too long to quickly bundle away out of the wind given the deck arrangement, you'd need those lazyjacks...or you'd need several decidedly un-lazy Jack Tars aboard to manhandle the thing in any sort of breeze!

Anyway, to the original question, it can be seen in the many splendid photos of Faering Cruiser that rigging lazyjacks on a balanced lug wouln't require additional mast height.

Laszlo, is there a video of you lowering the sail out there somewhere which might help illustrate the technique and how the lazyjacks play into it?

.....Michael

P.S.  That Faering Cruiser of yours is a lovely boat, by the way.  If I ever wanted another trailer boat, I'd have to give that design some serious consideration.  Be a swell way to cruise the islands of Georgian Bay, the coastal waters of North Carolina, the shallow waters of Florida's Big Bend, Kentucky Lake, and many other places to which I've been with other boats, never mind the countless other places of which I've only dreamed...so far.  <;-)

   Thanks for the replies,once I get her on the water l'll see how hard it is to deal with the sail. The fewer lines the better for me

Gramps,

No video, but there's almost nothing to film. Step 1 - tighten up the lazyjacks by pulling a single lanyard through a cam cleat. Step 2 - release the sail by uncleating the main halyard,

That's it. The sail comes down between the lazyjacks and is ready for furling, reefing, whatever.

Going the other way is just as easy. Pull the main halyard until the yard is where you want it and cleat it. Loosen the lazyjack halyard.

Laszlo

  I will just add that adding the lazyjacks made sailing solo markedly better.  I can drop the sail in seconds without having to keep it from swinging off the side of the boat. It is also held off the thwarts and can be easily raised to allow rowing. I have led my lines (downhaul, halyard, and lazyjack halyard) through blocks and cleats on the mast thwart which signifacantly reduces any confusion over which line is which; they are also different colors.  Barry