Step 1: Recall what Grignard reagents do.
A Grignard reagent adds to an aldehyde or ketone and, after water workup, gives an alcohol. The number of carbons on the carbonyl decides the alcohol type.
Step 2: Find X.
Ethanal (an aldehyde) reacts with isopropyl magnesium bromide to give a secondary alcohol. So $X$ is a secondary alcohol.
Step 3: Find Y.
Propanone (a ketone) reacts with ethyl magnesium bromide to give a tertiary alcohol. So $Y$ is a tertiary alcohol.
Step 4: Test statement I (dehydration).
Tertiary alcohols lose water most easily, so dehydration ease is $Y>X$. Statement I is correct.
Step 5: Test statement II (acidity).
A secondary alcohol is a little more acidic than a tertiary one because fewer electron pushing alkyl groups, so acidity is $X>Y$. Statement II is correct.
Step 6: Test statement III (Lucas).
The Lucas reagent reacts faster with tertiary alcohols, so it should be $Y>X$, making statement III wrong. So correct are I and II only. \[ \boxed{I,\ II\ only} \]