Both are pre-modern era romance dramas. Lady & Liar is set in 1930s China while the Suparburoot Chuthatep series is set in 1950s Thailand. So both feature period costumes, sets & culture, especially of the upper-class, which is just really gorgeous.
Both feature main female leads who come from a poor background and having to scrape a living with a single parent i.e. father, who is ill and needs help. Therefore both female leads, as filial and loving daughters, take on work which causes them to cross-paths with the male lead.
Both male leads are from old, established, wealthy and powerful families and have high standing in society. Both male leads fall in love almost at first sight when they met the female lead and are rather single-minded in pursuing their ladies.
Both shows have crazy, obsessive second female leads, and sleazy antagonists which provide conflict to the shows.
Note: "Khun Chai Puttipat" is Part 3 on a series of 5 brothers (it focuses on the 3rd brother's romance). It can be watched as a stand-alone, but it would help immensely if you read the synopsis of the first 2 brothers ("Khun Chai Taratorn" and "Khun Chai Pawonruj"), to provide some background and context.
Alternatively, you could also watch the other brothers' shows because they all have different conflicts, settings and personalities which makes each show unique and compelling.