All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.
First of all, it should be mentioned that whoever is able to delay the treatment of his teeth until the night during Ramadan and is not harmed by doing so, then he should delay it. That is because treating his teeth during the day could have some side effects which may force him to break his fast. However, if he could not delay the treatment and he is very much in need for it, then it is permissible for him to do so. Allaah Says (what means): {Allaah does not want to place you in difficulty.} [Quran 5:6]. In this case he may seek treatment during the day in Ramadan but he should not break his fast, and he should endeavor not to swallow anything during the treatment. Furthermore, taking an injection does not invalidate one's fast because it is neither food nor drink, nor is it a substitute for food or drink, and it does not reach the stomach trough the mouth or nose.
As regards limewater reaching the throat, if one predominantly thinks that something reaches his throat and is unable to spit it out, then he should not undergo this treatment unless he is sick a sickness which allows him to break the fast. Therefore, if one swallows what is mentioned in the question then his fast is void and he should make it up.
However, if it is very uncommon for someone to swallow this limewater and one tried his best to prevent anything from reaching his throat, yet something does reach his throat unintentionally, then this does not invalidate his fast. Allaah Says (what means): {So keep your duty to Allaah and fear Him as much as you can.}[Quran 64:16]. Moreover, the Prophet said: "Exaggerate when rinsing your nose unless you are fasting." [Abu Daawood, At-Tirmithi, Ibn Maajah & An-Nasaa'ee]. Therefore, whoever does not exaggerate in rinsing his nose when performing ablution while fasting, yet some water reached his throat, his fast does not become void.
Allaah Knows best.