Is LiOH a weaker base than NaOH?
In Proton Affinities of the Alkali Hydroxides J. Am. Chem. Soc., 1969, 91, pp 2810–2811, it is shown that gas phase affinities in $\pu{kcal/mol}$ are:  


  
  $\ce{LiOH}$: 240.7
  $\ce{NaOH}$: 247.6
  $\ce{KOH}$: 262.6 
  $\ce{CsOH}$: 269.2
  


So, yes, $\ce{LiOH}$ is weaker, at least in the gas phase.   

In aqueous solution, ACIDITY FUNCTIONS FOR STRONGLY BASIC SOLUTIONS Chemical Reviews volume 66, pages 119-131:  


  the order of basicity for the same molarity of aqueous solution, $\ce{LiOH &lt; NaOH &lt; KOH}$. 


For example, for a $\pu{1M}$ solution, the acidity function (H) is: 


  
  $\ce{LiOH}$: 13.48
  $\ce{NaOH}$: 14.01, 14.16 (two different measurement techniques)
  $\ce{KOH}$: 14.17
  


So in both the gas and aqueous phases, $\ce{LiOH}$ is a weaker base than $\ce{NaOH}$.