I gave my boy at KKH too and I noticed the same thing! I think it's their baby wash or lotion they use during the routine checks and cleaning, but honestly I never managed to ask the nurses directly what brand it was.
Maybe try asking the nurses next time your baby goes for a procedure or test, they're usually quite helpful about these things. Some mums swear it's just the standard hospital-grade products they use, but that lavender scent is really quite lovely isn't it.