Does exchange rate of local currency relative to US dollar mean LOC/USD or USD/LOC ?
LOC/USD and USD/LOC are currency pairs. Whatever currency comes first is known as the base currency. The currency that comes second is known as quote currency. For major currency pairs, the format of the currency pair is based on established priority. For example, EUR has the highest established priority and thus is almost always shown as the base currency.
Currency pairs quotes work such that one unit of the base currency can be exchanged for quoted amount of the quote currency (hence the name "quote currency"). For example, LOC/USD 6.25 means that one LOC can be exchanged for 6.25 USD. USD/LOC 0.16 means that one USD can be exchanged for 0.16 LOC.
Whenever people say "local currency relative to US dollar", that usually should be parsed as "[base currency] relative to [quote currency]", and thus it would be LOC/USD. A similar interpretation applies for "local currency quoted against the US dollar" (LOC/USD). Another hint is that most "minor currencies" are quoted against the US dollar.