While Apple generally says that iPhone service/repair may be limited to the country in which the phone was originally distributed, there shouldn't be an issue with a universal replacement part like a screen assembly or a battery. That being said, the only replacement is with a complete screen assembly including the display, digitizer, and glass. Also - there may not be a guarantee of how long it might take depending on availability of technicians and especially if the replacement part needs to be ordered. That might be something worth considering if it might take longer than the time that your friend has in Singapore.
Also - all iPhone X models (including the XS Max) have an OLED (not an LCD) display.
Here are the prices for the Apple Store in Singapore (including taxes):
iPhone Screen Repair & Replacement - Official Apple Support