daijr: 嘘を言うこと。また，その人。

All the kokugos mention both the act and the person.
This isn't 形動 in any of the refs. I think adjectival use is quite informal and doesn't warrant an adj-na tag.
I think ウソつき can be hidden.

@@ -41 +41 @@
-<re_nokanji/>
+<re_inf>&sk;</re_inf>
@@ -45 +44,0 @@
-<pos>&adj-na;</pos>
@@ -47,0 +47,4 @@
+</sense>
+<sense>
+<pos>&n;</pos>
+<gloss>lying</gloss>

Usage of 付 seems to be irregular here

Google N-gram Corpus Counts
╭─ーーーー─┬─────────┬───────╮
│ 嘘つき　 │ 430,819 │ 56.5% │
│ 嘘吐き　 │  45,770 │  6.0% │
│ 嘘付き　 │   6,645 │  0.9% │ - sK
│ ウソ付き │   1,693 │  0.2% │ - sK
│ 嘘ツキ　 │   1,149 │  0.2% │
│ ウソ吐き │     468 │  0.1% │ - sK
│ 噓つき　 │     332 │  0.0% │
│ うそ付き │     119 │  0.0% │ - sK
│ 噓吐き　 │      37 │  0.0% │ - sK
│ うそ吐き │      27 │  0.0% │ - sK
│ 噓付き　 │       0 │  0.0% │
│ 噓ツキ　 │       0 │  0.0% │
│ うそつき │ 187,536 │ 24.6% │
│ ウソつき │  53,480 │  7.0% │ - nokanji; dropping restrictions
│ ウソツキ │  34,217 │  4.5% │
│ うそツキ │      64 │  0.0% │
╰─ーーーー─┴─────────┴───────╯

@@ -12,0 +13 @@
+<ke_inf>&sK;</ke_inf>
@@ -15,0 +17 @@
+<ke_inf>&sK;</ke_inf>
@@ -18,0 +21 @@
+<ke_inf>&sK;</ke_inf>
@@ -21,0 +25 @@
+<ke_inf>&sK;</ke_inf>
@@ -24,0 +29 @@
+<ke_inf>&sK;</ke_inf>
@@ -27,0 +33 @@
+<ke_inf>&sK;</ke_inf>
@@ -31,6 +36,0 @@
-<re_restr>嘘つき</re_restr>
-<re_restr>嘘吐き</re_restr>
-<re_restr>嘘付き</re_restr>
-<re_restr>うそ付き</re_restr>
-<re_restr>噓吐き</re_restr>
-<re_restr>うそ吐き</re_restr>
@@ -41,2 +41 @@
-<re_restr>ウソ付き</re_restr>
-<re_restr>ウソ吐き</re_restr>
+<re_nokanji/>