Origin of values in a steam table

@Chet Miller has already explained the origin of the values in the saturated steam tables.

In order to determine the values of the specific properties for the liquid vapor mixture, you need to be given the quality $x$ of the steam, which is the fraction of the mixture that is saturated vapor. Then, for example, the specific enthalpy of the steam mixture is

$$h=xh_{g}+(1-x)h_{f}$$

Where $h_{g}$ and $h_{f}$ are the specific enthalpies of the saturated vapor and saturated liquid respectively, from the steam tables. The same equation applies to $s$, $u$, and $v$.

Note that this is the same equation that you call the "lever rule" if you rearrange it and put $x$ on the left side of the equation.

To rephrase my query: Whether the Maxwell lever rule (which motivates the definition of quality), is actually used in obtaining values for the coexistence region in the steam table.

The term "lever rule" had a familiar ring to it, but I didn't remember any reference to in connection with the steam tables. Then I remembered the term lever rule being used in material science in analyzing binary phase diagrams of alloys.

FIG 1 shows the use of the rule in connection with the liquid and solid phases of an allow.

FIG 2 shows the equation for determining any given property of the liquid/vapor mixture ($v$, $u$, $h$, ore $s$)

Iv'e highlighted (boxed) the analogous equations.

So in answer to your question, the term "lever rule" is not actually used in connection with determining a property of the steam liquid/vapor mixture, given the quality, or determining the quality given the value of a steam liquid/vapor mixture. However, the approach actually used is definitely analogous to the lever rule.

Hope this helps.