why are lp-lp repulsions greater than bp-lp and bp-bp?
So, from Wikipedia article on VSEPR theory we read:


  The overall geometry is further refined by distinguishing between
  bonding and nonbonding electron pairs. The bonding electron pair
  shared in a sigma bond with an adjacent atom lies further from the
  central atom than a nonbonding (lone) pair of that atom, which is held
  close to its positively charged nucleus. VSEPR theory therefore views
  repulsion by the lone pair to be greater than the repulsion by a
  bonding pair. As such, when a molecule has 2 interactions with
  different degrees of repulsion, VSEPR theory predicts the structure
  where lone pairs occupy positions that allow them to experience less
  repulsion. Lone pair-lone pair (lp-lp) repulsions are considered
  stronger than lone pair-bonding pair (lp-bp) repulsions, which in turn
  are considered stronger than bonding pair-bonding pair (bp-bp)
  repulsions, distinctions that then guide decisions about overall
  geometry when 2 or more non-equivalent positions are possible.


As I said in my comment, the key point is given in the second sentence: the bonding pair shared in a bond lies further from the atom than a nonbonding pair of that atom which is held close to its positively charged nucleus. Consequently, lone pairs are closer to each other than any other combination of pairs (lone pair-bonding pair and bonding pair-bonding pair), and thus, repell each other more strongly.