Here's the evidence set out in order:
PIE had endings beginning with liquids. Some roots ending in
liquids. Therefore some derivatives of roots ending in liquids should
show combinations of liquid+liquid.
However, there has been little evidence put forth that any such
words in PIE times survived and were attested in any IE language.
Those that show R+R in IE languages are usually regular(ized?)
derivatives or compounds that weren't necessarily of PIE origin (like
supellex < super+ *Leghtlyos).
However, I feel I have found some. The roots *bhel+ 'swell' and
*dhel+ 'rise/grow out of, spring up (used of shoots, branches, etc.)
might have derivatives with the diminutive *+Lo+ (as in L -ulus, Gk
-los / -al(l)os, Gmc. *-(i)la-).
*dhl,+Lo+ 'little growth, shoot' > thal(l)os 'twig, sprout, etc.'
*bhl,+Lo+ 'little swelling, testicle, penis, etc.' > Gk phallos,
phalos 'horn on a helmet'
These show both -ll- and -l- from *-ll- but Gk -ll- from -ln- or
-ly- or -sl-, etc., only appear as -ll-. This indicates that -ll- >
-l- (opt. or dia.) was early, before -ln- > -ll-, etc.
Further ev. that this is old but not PIE comes from:
*kàrttlós > *kàrt_los > *kàrtllos > kartal(l)os 'basket'
The stem *kart+ 'bend, plait, weave, etc.' + *-tlo- creates cluster
rttl which is likely to be changed; when one t drops the open slot is
filled by l. Since rtll is also odd, it was broken up by inserting a
before ll.
The same as with diminutives in -al(l)os or -ax after clusters so no
*krustlos or *portkos. So:
*d.óru+sèdó+ > *d.(e)rusdó+ 'tree-sitting, thrush'
*kYórud.rusdó+ 'crested perching bird' >
*kYórud.usdó+ > *kórud_zdo+ >
kórudos 'crested lark'
*kYórud.rusdLó+ (a diminutive) >
*kYórud.usdLó+ > *kórud_zdLo+ > *kórud_Lo+ >
*kórudLLo+ > korudallis, -alos, etc. 'crested lark'
Dissim. of u-u creates cluster dzdL which is changed > d_L; when the
open slot is filled by L and this broken up by inserting a before LL.
The existence of L in PIE is shown by e>a by L, changes of a>o by L
in Greek (like Armenian, which is clearer, but which turns l>L and L>l
in many places first), and L,>u before a dental. This is seen in
cognates like:
*bhl,Lo+ >> *bullo: 'bowl, bud, etc.'
*bhl,u+ >> *pholw+is > L follis 'ball, cushion inflated with air' (u-
> wi- stem like *ml,du+ > mollis, etc.)
or
*bhelLos bhelu+ > *bhollos bholu+ mix> *ballu+ > ball
maybe
*dhl,Lo+ > *dalaLa+ > dalar 'green, fresh'
if dissimilation.
The existence of clusters like l,L and r,n in a syllable in PIE is
shown by *bhl,Lon.+ 'a swollen animal' with nom. *bhl,Lo:n. and weak
stem *bhl,Ln.+ in cognates like:
*bhl,Lon.+ > *buLan+
*bhl,Ln.+ > *buLn+ > *bull+ (and mix with above)
*bhl,Ln.+ix (fem. voc.) > *bhl,Ln,ya > pHál(l)aina
*bhl,Ln.i:x (fem. nom.) > *bhl,n.i: > blini
*bhl,Lon.+ (m.) > *bhal-won. >
*bal-wan.+ ' ~ snake, dragon ("worm")'
> Alb. bollë
> *bal-awn.+ > Romanian balaur
The l,L is necessary in blini to prevent l, > al before C+sonorant in
the next syl., then it drops between C_C and l,>li as in most
environments. In balaur L>w after l (as it does in certain positions
in PIE) and then metathesis.
bhl,-Lon.+ ... bhl,L-n.ix
bhal-Lon.+ ... bhl,L-n.ix
bhal-Lon.+ ... bhl,-n.ix
bhal-Lon.+ ... bhli-n.ix
bhal-won.+ ... bhli-n.ix
bal-wan.+ .... bli-n.i:
etc.