Remember, every second you spend in Lua is a second that the Server thread, Connection thread, and possibly one or more Emerge threads stay at a complete standstill! For this reason, intensive mods should designed with speed in mind.
N.B.
Many of these tips are specific to neither Lua nor Minetest.

Using Script API

Profiling

Very simple; no reason not to do so:

local t1 = os.clock()
--... work here ...
print(string.format("elapsed time: %.2fms", (os.clock() - t1) * 1000))

Compare results often to identify bottlenecks before they become harder to find

Loop ordering

Always use z, y, x ordering unless there's a good reason not to.

Keeps cache coherency
Opens opportunity to use simple arithmetic to calculate indicies

Prefer local variables

Should usually recompute variable contents instead of computing once and storing in a global variable
For most minor computations, the benefit of local access outweighs the cost of re-computing their contents.
Of course, the code in concern should be profiled instead of blindly following this general rule of thumb.

Use separate variables when possible instead of tables

Even though putting associated variables inside of tables may keep things more orderly, the cost associated with performing a key lookup on access is high compared to a local variable reference.
Some benchmarks have shown the opposite to be true when using LuaJIT, this must be verified.

Avoid having to re-enter the C++ side by calling API when not needed

Although Lua is quite slow compared to native code, the amount of time spent in switching could be much greater.
Again, the developer's discretion and profiling is needed to determine what the best course of action is.

Array index calculation

"Convenience" functions such as VoxelArea:index() are very attractive for simplicity's sake, but should not be used if maximizing speed is desired.
Try to use simple arithmetic like addition and subtraction for calculating array indices.
To deal with gaps in between multi-dimensional arrays:

Keep a 'base' index variable that has the 0th sub-index of the current outer loop's index
Add the stride length added to it per iteration of the outer loop
Increment a copy of that variable within the inner loop
Repeat for each dimension

This way, costly multiplications in the innermost loop can be eliminated.
Sample of a very fast loop done in this manner:

local idx_z_base = initial_index_offset
for z = z0, z1 do
	local idx_y_base = idx_z_base
	for y = y0, y1 do
		local i = idx_y_base
		for x = x0, x1 do
			-- ... work here ...
			i = i + 1
		end
		idx_y_base = idx_y_base + y_stride
	end
	idx_z_base = idx_z_base + z_stride
end

Use iteration instead of recursion

e.g. this:

-- depends on vector_extras

local set = vector.set_data_to_pos
local get = vector.get_data_from_pos
local remove = vector.remove_data_from_pos

local function get_tab2d(pos, func, max)
	local z,y,x = vector.unpack(pos)
	local tab = {{z,x}}
	local tab_avoid = {}
	set(tab_avoid, z,x,0, true)
	local tab_done,num = {pos},2
	local n = 1
	while n do
		local z,x = unpack(tab[n])
		for i = -1,1,2 do
			for _,p2 in pairs({
				{z+i,x},
				{z,x+i},
			}) do
				local z,x = unpack(p2)
				if not get(tab_avoid, z,x,0)
				and func({x=x, y=y, z=z}) then
					set(tab_avoid, z,x,0, true)
					tab_done[num] = p2
					num = num+1
					if max
					and num > max then
						return false
					end
					table.insert(tab, {z,x})
				end
			end
		end
		tab[n] = nil
		n = next(tab)
	end
	return tab_done
end

Writing Script API

When working with arrays, use lua_rawgeti()/lua_rawseti()

These work on plain integer indexes rather than field names and perform faster.

Prefer lua_newtable() to lua_createtable()

It has been observed that lua_newtable() is generally faster than lua_createtable() by a rather wide margin.

This might seem counterintuitive, as lua_createtable() preallocates a known amount of memory in bulk to save steps, but it has a very negative effect on the cache for situations where the performance improvement would have otherwise made a difference.

Lua Optimization Tips

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