Extract a pattern from multiple lines in a file

I have a file that has some lines starts with *
I want to get these lines, then get the word between "diac" and "lex".

ex.
file:

;;WORD AlAx
*0.942490 diac:Al>ax lex:>ax_1 bw:Al/DET+>ax/NOUN+ gloss:brother pos:noun prc3:0 prc2:0 prc1:0 prc0:Al_det per:na asp:na vox:na mod:na gen:m num:s stt:d cas:u enc0:0 rat:y source:spvar stem:>ax stemcat:N0F
--------------
;;WORD gyr
*0.983117 diac:gayoru lex:gayor_1 bw:+gayor/NOUN+u/CASE_DEF_NOM gloss:not;other pos:noun prc3:0 prc2:0 prc1:0 prc0:0 per:na asp:na vox:na mod:na gen:m num:s stt:c cas:n enc0:0 rat:y source:lex stem:gayor stemcat:N

Desired output:

Al>ax
gayoru

I am not sure if I should use sed or grep. Have been trying for a while, with this command:

grep -A 3 -o ':.* lex:' boo

I get:

:Al>ax lex:

Thank you in advance!

$ nawk -F"[ :]" '/^\*/{for(i=1;i<=NF;i++)if($i~/diac/){print $(i+1);next}}' input.txt
Al>ax
gayoru

if you dont have nawk, then try with awk

sed -n 's/^*.*diac:\(.*\) lex:.*/\1/p' infile

awk -F"diac:|lex" '/^*/ {print $2}' infile

On Aix * must be escaped

#awk -F"diac:|lex" ' /^\*/ {print $2}' file