That is a classic F1 F1 question. It's proprietary software and BBG offers a dedicated help desk.
DTK is not available for free via BLPAPI. Connecting DLIB to an API requires a premium service called Mars API (which will work via DAPI, but also BPIPE and the like, depending on your needs). I suggest you reach out to your sales rep and ask him / her about this feature if you are willing to pay (this service is quite expensive as it is an enterprise solution).
You can have a look at some code snippets if you search for DOCS MARS API
on the terminal. DOCS 2097583
is for MARS API in general (architecture, delivery channels, ...)
MARS API leverages the same libraries when setting elements and making requests as BLPAPI, just that DLIB (BLAN) has a LOT more handle parameters and overrides compared to standard BLPAPI. DOCS 2096689
is for MARS API with DLIB specifically.
When you say you need a strike solver, for what products exactly? I find it hard to believe BLAN will help you here, because hand written BLAN has no solver capabilities as much as I know. Also pulling option prices with BLAN will be substantially simpler with DTK (it is already a wrapper) because there are no available wrappers for Mars API (it is not widely available like the standard BLAPI desktop requests that are "free" for every BBG user).
I am not sure about OVME but the infrastructure should be similar to OVML. For OVML, you can request an override for strike and expiry date (I think your eligibility to use this and potential costs depend on some criteria, but F1 F1 or your sales rep should be able to help with that too). Aftwards, you can use any saved deal, change expiry and strike as you wish, and iterate that way to a desired option value. This will not only be easier to implement but also substantually faster and more reliable compared to DLIB which relies on Monte Carlo runs. Below is an example (bear in mind, it WILL NOT work if you do not have the override priviledge granted).
The field for expiry date is called OP002 – OPT_EXPIRE_DT.

Edit
DLIB BLAN is essentially OCAML. You can use while loops.
let sum = ref 0;
let cnt = ref 1;
while !cnt <= 10 do
let i = !cnt;
sum := !sum + i;
cnt := i + 1;
done;
!sum
Should work for example.
BLPAPI has a very detailed documentation on WAPI. However, I reiterate that you could simply use the OV override instead of DLIB. It also works directly with existing BLAPI wrappers on the web (it is a simple BDP formula with overrides). All you need is a dummy ticker (saved OV deal) for each underlying and product (call, digital etc). Afterwards you can override dates and strike to retrieve the corresponding value. For example like this.
=BDP("Ticker","OPT_THEOR_VALUE", "OPT_STRIKE_PX=3930.0800", "OPT_VALUATION_DT=20220520", "OPT_EXPIRE_DT=20220811")
where Ticker refers to either "OVME_ID Index" or "OVME_ID Equity".
You can refresh whenever you tell the API. It is miles faster than an equivalent BLAN solution (and almost surely more accurate too).