"look-up tables", "look up tables" or "lookup tables"

To look up is a verb, and only a verb. A verb cannot be used to qualify a noun like an adjective or another noun can.

A lookup is a noun. Nouns can be used to qualify other nouns like adjectives can.

A lookup table is a type of table. That's two nouns with the first being a qualifier telling us more about what type the second one is.

This is a general rule in English that the two-word version with a plain verb followed by an adverbial particle or preposition is a verb, whereas the single-word version is a noun:

• to back up -> a backup
• to come back -> a comeback
• to follow up -> a followup
• to lock down -> a lockdown
• to log in -> a login
• to look up -> a lookup
• to set up -> a setup
• to start up -> a startup
• to work out -> a workout

A further distinction can be made with hyphenated versions, which are primarily to be used as adjectives:

• to follow up -> a follow-up email

This seems to be getting a bit old-fashioned or formal perhaps and has been declining for a long time, being replaced by the single-word versions.

The current fad of replacing all two-word versions with single-word versions is much more recent and has been blamed on both spellcheckers and the IT community as it's much more common with terms used in IT though it has spread into terms outside IT now too.

Note that so far it only happens when both verb and noun forms are common. When only a verb exists nobody makes this error. Hence you will see "I will comeback" but you never see "I will goback" because even though "to come back" and "to go back" are both legitimate verbs, only "a comeback" is a legitimate noun.

There's a website with a big list of these errors on 'notaverb.com'

As words or phrases enter the language, they tend to steadily migrate from separate (look up), to hyphenated (look-up), to one word (lookup). I would be of the view that lookup has been around long enough to be one word (as "instore" now seems to be).

However I don't think followup is one word - it looks odd, so follow-up would be my preference. And "the build-up of a lookup table" doesn't sound right to me either - I would probably say "the build of a lookup table" or "the building of a lookup table", or "the populating of a lookup table".

I would write lookup table, since lookup is a term accepted by computer people. For example:

... the lookup table creation. ... building the lookup table. ... create the lookup table.

depending on context.