Moon parameters:

mu=4902.7779 km^3/s^2

re=1738.14 km

Apollo LM pre-PDI orbit:

ha=60 nmi

hp=8 nmi (PDI was at perilune)

Using 1 nmi=1.852 km,

ra=re+ha*nmi=1849.26 km

rp=re+hp*nmi=1752.96 km

a=(ra+rp)/2=1801.1 km

and vis-viva equation gives:

vp=sqrt(mu*(2/rp-1/a)=1.694 km/s

which was the speed of the LM with respect to a non-rotating moon at PDI (moon rotates very slowly so can be neglected).

Note that the 2.38 km/s given by the site is not applicable in this situation because that's essentially the escape velocity of the moon, while for Apollo the LM did not begin descent from an escape trajectory, but rather from a low elliptical orbit (for which the CSM did the heavy lift of LOI and, for the later missions, DOI).

Apollo LM parameters:

m0=14696 kg

mp=8165 kg

Isp=311 s

so:

mf=m0-mp=6531 kg

and using 9.80665 m/s^2 for g0 gives:

ve=3.05 km/s

so the rocket equation gives:

dv=ve*ln(m0/mf)=2.47 km/s

as the theoretical delta-v of the LM descent stage.

There will be some gravity losses during descent, especially after throttle-down and during hover, but it's clear that the LM had the muscle for the job with a bit of hover margin to spare.