The short answer:
A ‘Lintel’ is a horizontal header beam supported by two vertical posts on either end.  It supports openings such as a window or door.
A ‘Lally’ is a concrete filled column that supports long spans of beams.
The long answer:
I’ve been toying with the idea of starting a design business & even went back to school for interior design, but the day the third random person knocked on my door asking me, “Who ‘picked the colors for this house?”, I felt that the time is NOW…let’s dive in & do this!
So, what started as a hobby grew into a business, which meant we needed a name, and fast!  We tried the typical ‘list of favorite words’.  We spent hours on the thesaurus trying to find different ways to say, ‘inspiring, creative, inviting, interior design, etc’.  All the obvious names had all ready been taken.   We couldn’t just settle for something predicatable.  Sure, Barbara’s last name would be perfect ‘Holmes, Holmestead-designs’…but our designs are about each individual we work with.  We didn’t want the name to be about ‘us’. 
After pondering countless word combos, a scene from ‘Mr. Blandings Builds His Dream House’, came to mind.  It was a scene where the character, played by Cary Grant, gets asked the puzzling question, “Do you want the Lintels between the Lallies rabbeted?”  It is a comical scene that always brings a smile to our faces. 
A lintel is a beam that runs horizontally across two lally columns, usually for a home’s entrance.  And so, long story short, L & L is set out to make you love your home the moment you cross your threshold – your Lintels & Lallies.

BTW-if you haven’t watched ‘Mr. Blandings Builds His Dream House’, I highly recommend it! 😉