You are spot on WRT the process for determining alkalinity but note that the end point pH depends on the ISO if you are using their procedure or your choice if you are using AWWA's. IOW it doesn't matter as long as you specify what the end point pH is. It is usually between 4.3 and 4.5.
The other thing you need to know is the strength of the acid in mEq/L (miliequivalents per liter). The problem with lactic acid is that it's strength depends on the end point titration pJ. The strength of 88% w/w lactic acid is 8.66 mEq/L (written 8.66 N) at pH 4.3, 9.15 N at pH 4.4 and 9.55 N at pH 4.5. For this reason perhaps lactic isn't the best choice (it's not really a strong acid) but it is doable. The strengths above are calculated assuming that you have exactly 88% lactic acid and you probably don't. What you actually have is what you actually have.
In an actual titration 100 mL is generally considered a convenient sample size to work with and with 0.1 L of sample 0.1 N acid means that the alkalinity is numerically equal to the number of mL it takes to get that 0.1 L from whatever pH it comes out of the tap at to the end point pH. In the US we multiply the mEq/L by 50 and call the result alkalinity in ppm as CaCO3.
88% lactic acid is way too strong (this is a separate meaning for 'strong' as it refers her to concentration) for your titration. But of course you can dilute down to 0.1 N with DI water and go from there. This, of course, involves measurement of dilution water and small amounts of acid of unknown (precisely) strength. So what you do is 'standardize' your dilute acid against something whose strength is exactly known. The only thing like that you are going to find in the LHBS is the 0.2 N NaOH that they sell for vintners use in determining titratable acidity of their wine musts. You can also buy 10% phosphoric acid at an LHBS which is about 1 N. It isn't of constant strength over pH either but is more so than lactic acid so that may be a better choice. You could dilute it 10:1 with DI water and standardize with the NaOH. There is a big problem with NaOH, however, and that is that it sucks CO2 out of the air thus reducing its strength the longer it is exposed to air.
It is far, far less trouble, IMO, to buy a bottle of 0.1 N sulfuric acid (constant normality over the end point range) from Hach for about $12 (IIRC) and not have to do any dilution or standardization. Pay them to do that for you!
Pop over to
http://www.wetnewf.org/pdfs/measuring-alkalinity.html to read more about how to measure alkalinity.
Now lets ask the fundamental question: "Why do you want to measure the alkalinity of your water?" The real answer to that is so that you will know how much acid you will need to add to your mash or sparge in order to overcome that alkalinity. You can, of course, titrate a volume of your water to mash pH end point using you lactic acid. Use a syringe or eyedropper to dispense. If you want to mash to pH 5.4 add drops of 88% lactic acid to a gallon until it's pH reaches 5.4. The result is your alkalinity to pH 5.4 (your choice of endpoint) in units of drops/gallon. You don't really care how that relates to mEq/L, ppm as CaCO3, dH or any other unit as when you go to treat you water for brewing then you simply multiply the drops/gal by the volume in gal and add that many drops.